{
  "title": "Loci Basics Through Constructions - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the locus of points at a fixed distance from a fixed point?", "options": {"A": "Line", "B": "Circle", "C": "Square", "D": "Triangle"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "The locus of points equidistant from two fixed points is:", "options": {"A": "Angle bisector", "B": "Perpendicular bisector", "C": "Parallel line", "D": "Circle"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "What is the locus of points at a fixed distance from a fixed line?", "options": {"A": "Two parallel lines", "B": "Circle", "C": "Perpendicular line", "D": "Single line"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "The locus of points equidistant from two intersecting lines is:", "options": {"A": "Perpendicular bisector", "B": "Angle bisector", "C": "Parallel lines", "D": "Circle"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "If a point moves maintaining equal distance from endpoints of segment, its locus is:", "options": {"A": "Line parallel to segment", "B": "Perpendicular bisector", "C": "Circle with segment as diameter", "D": "Angle bisector"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "The locus of points 3 cm from point P is:", "options": {"A": "Line 3 cm long", "B": "Circle radius 3 cm", "C": "Square side 3 cm", "D": "Triangle"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Locus of points 2 cm from line AB consists of:", "options": {"A": "One line", "B": "Two lines", "C": "Circle", "D": "Point"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "What shape describes all points 4 cm from point O?", "options": {"A": "Square", "B": "Line", "C": "Circle", "D": "Rectangle"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "The locus of center of a rolling circle is:", "options": {"A": "Circle", "B": "Line", "C": "Point", "D": "Spiral"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Points equidistant from sides of an angle lie on:", "options": {"A": "Perpendicular bisector", "B": "Angle bisector", "C": "Parallel line", "D": "Circle"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "The locus of points 5 units from origin in coordinate plane is:", "options": {"A": "Line x=5", "B": "Circle radius 5", "C": "Square", "D": "Line y=5"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If a point is always 3 cm from line L, its locus is:", "options": {"A": "One line", "B": "Two parallel lines", "C": "Circle", "D": "Point"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Locus of points equidistant from points (2,3) and (2,7) is:", "options": {"A": "x=2", "B": "y=5", "C": "x=5", "D": "y=2"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Points at constant distance from a fixed point form:", "options": {"A": "Straight line", "B": "Circular path", "C": "Parabolic path", "D": "Elliptical path"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "The locus of midpoints of all chords of given length in a circle is:", "options": {"A": "Circle", "B": "Line", "C": "Concentric circle", "D": "Point"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Locus of points equidistant from x-axis and y-axis is:", "options": {"A": "Lines y=x and y=-x", "B": "x-axis only", "C": "y-axis only", "D": "Origin only"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "A point moves so its distance from (0,0) is always 4. Its locus:", "options": {"A": "x²+y²=4", "B": "x²+y²=16", "C": "x+y=4", "D": "x=4,y=4"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Locus of centers of circles touching two parallel lines is:", "options": {"A": "Line parallel to them", "B": "Line perpendicular to them", "C": "Circle", "D": "Point"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Points 2 cm from point P and 3 cm from point Q: how many such points typically?", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Locus of vertices of right triangles with fixed hypotenuse is:", "options": {"A": "Line", "B": "Circle with hypotenuse as diameter", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "Find locus of points equidistant from points A(2,3) and B(6,3).", "options": {"A": "x=2", "B": "x=4", "C": "y=3", "D": "y=4"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Construct locus of points 3 cm from line segment AB=5 cm. What shape?", "options": {"A": "Two parallel lines+two semicircles", "B": "Circle", "C": "Rectangle", "D": "Two lines only"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Locus of points equidistant from two concentric circles is:", "options": {"A": "Another concentric circle", "B": "Line through center", "C": "Circle midway between", "D": "Point"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Point P moves such that PA=PB where A(0,0), B(4,0). Locus of P is:", "options": {"A": "x=0", "B": "x=2", "C": "y=0", "D": "y=2"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Find equation of locus of points 5 units from (2,-1).", "options": {"A": "(x-2)²+(y+1)²=5", "B": "(x-2)²+(y+1)²=25", "C": "x²+y²=25", "D": "(x+2)²+(y-1)²=25"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Locus of points equidistant from lines y=3 and y=7 is:", "options": {"A": "y=4", "B": "y=5", "C": "y=10", "D": "x=5"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Construct locus of points 2 cm from point O and 3 cm from line L. Maximum points of intersection?", "options": {"A": "0", "B": "2", "C": "4", "D": "Infinite"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "Point moves so sum of distances from (3,0) and (-3,0) is 10. Its locus:", "options": {"A": "Circle", "B": "Ellipse", "C": "Line", "D": "Parabola"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Locus of centers of circles touching two intersecting lines is:", "options": {"A": "Angle bisectors", "B": "Perpendicular bisector", "C": "Parallel lines", "D": "Circle"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Find locus of points equidistant from x-axis and point (0,2).", "options": {"A": "y=1", "B": "Parabola x²=4(y-1)", "C": "Line x=1", "D": "Circle"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Construct locus of points equidistant from sides of 60° angle. This locus is:", "options": {"A": "Line making 30° with each side", "B": "Perpendicular line", "C": "Circle", "D": "Two lines"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Locus of midpoints of equal chords of circle is:", "options": {"A": "Concentric circle", "B": "Diameter", "C": "Chord", "D": "Tangent"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Point P moves so its distance from (1,2) is twice distance from (4,6). Locus is:", "options": {"A": "Circle", "B": "Line", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Locus of points 3 cm from circle of radius 5 cm is:", "options": {"A": "Circle radius 8 cm", "B": "Two circles radii 2 and 8 cm", "C": "Circle radius 3 cm", "D": "Annular region"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Construct locus of points equidistant from two parallel lines 6 cm apart.", "options": {"A": "Line 3 cm from each", "B": "Two lines", "C": "Circle", "D": "Point"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Locus of points where ∠APB=90° for fixed A and B is:", "options": {"A": "Line perpendicular to AB", "B": "Circle with AB as diameter", "C": "Perpendicular bisector", "D": "Angle bisector"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Find locus of points equidistant from (a,0) and (-a,0).", "options": {"A": "x=0", "B": "y=0", "C": "x=a", "D": "y=a"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Point moves so its distance from y-axis is distance from (2,0). Locus:", "options": {"A": "Parabola", "B": "Circle", "C": "Line", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Locus of points at given distance from given line and circle may have intersection points:", "options": {"A": "0,2,or4", "B": "Always 2", "C": "Always 4", "D": "Infinite"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Construct locus of points equidistant from vertices of triangle. This point is:", "options": {"A": "Centroid", "B": "Circumcenter", "C": "Incenter", "D": "Orthocenter"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "Locus of points equidistant from sides of triangle is:", "options": {"A": "Centroid", "B": "Circumcenter", "C": "Incenter", "D": "Orthocenter"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Point moves keeping equal distance from coordinate axes. Its locus:", "options": {"A": "x=y and x=-y", "B": "x=0", "C": "y=0", "D": "x²+y²=1"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Locus of centers of circles passing through two fixed points is:", "options": {"A": "Line", "B": "Circle", "C": "Point", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Find locus of points P such that PA²-PB²=constant for fixed A,B.", "options": {"A": "Line perpendicular to AB", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Construct locus of points 2 cm from circle radius 3 cm.", "options": {"A": "Two circles radii 1 and 5", "B": "One circle radius 5", "C": "Annulus", "D": "Point"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Locus of points where difference of distances from two fixed points is constant:", "options": {"A": "Circle", "B": "Ellipse", "C": "Hyperbola", "D": "Parabola"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "Point moves so sum of squares of distances from axes is 25. Locus:", "options": {"A": "Circle", "B": "Ellipse", "C": "x²+y²=25", "D": "x²+y²=12.5"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "Locus of points equidistant from three non-collinear points is:", "options": {"A": "Point", "B": "Line", "C": "Circle", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Construct locus of points equidistant from sides of square.", "options": {"A": "Point (center)", "B": "Circle", "C": "Lines", "D": "Square"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Locus of midpoints of chords of circle through fixed point is:", "options": {"A": "Circle", "B": "Line", "C": "Another circle", "D": "Point"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Point moves so distance from origin equals distance from line x=4. Locus:", "options": {"A": "Parabola", "B": "Circle", "C": "Line", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Locus of points P such that area of triangle PAB is constant:", "options": {"A": "Line parallel to AB", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Construct locus of points equidistant from two intersecting lines making 70° angle.", "options": {"A": "Line at 35° to each", "B": "Two lines", "C": "Circle", "D": "Point"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Locus of points at constant ratio of distances from two fixed points is:", "options": {"A": "Circle (Apollonius circle)", "B": "Line", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Find locus of points 3 units from line x=2.", "options": {"A": "Lines x=-1 and x=5", "B": "Line x=5", "C": "Circle", "D": "Point"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Locus of centers of circles touching given circle externally at given point is:", "options": {"A": "Line", "B": "Circle", "C": "Ray", "D": "Point"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "Point moves so its distance from (0,2) is equal to its distance from x-axis. Locus:", "options": {"A": "Parabola", "B": "Circle", "C": "Line", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Locus of vertices of triangles with same base and equal area is:", "options": {"A": "Line parallel to base", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Construct locus of points equidistant from endpoints of diameter.", "options": {"A": "Perpendicular bisector of diameter", "B": "Circle", "C": "Diameter itself", "D": "Point"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Locus of points forming right angle with endpoints of segment is:", "options": {"A": "Circle with segment as diameter", "B": "Perpendicular bisector", "C": "Line", "D": "Point"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Find locus of points equidistant from lines 3x+4y=5 and 3x+4y=15.", "options": {"A": "Line 3x+4y=10", "B": "Line 4x-3y=10", "C": "Point", "D": "Circle"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Locus of points at distance d from line and D from point has maximum intersections:", "options": {"A": "4", "B": "2", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Point moves so product of distances from axes is constant. Locus:", "options": {"A": "Hyperbola", "B": "Circle", "C": "Line", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Locus of centers of circles touching given line at given point is:", "options": {"A": "Line perpendicular to given line", "B": "Circle", "C": "Parallel line", "D": "Point"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Construct locus of points 4 cm from point O and equidistant from two lines.", "options": {"A": "At most 4 points", "B": "Circle", "C": "Line", "D": "Infinite points"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Locus of points with constant sum of distances from two fixed points is:", "options": {"A": "Ellipse", "B": "Circle", "C": "Line", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Find locus of points where difference of distances from (5,0) and (-5,0) is 6.", "options": {"A": "Hyperbola", "B": "Ellipse", "C": "Circle", "D": "Line"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Locus of points equidistant from vertices of right triangle lies on:", "options": {"A": "Hypotenuse midpoint", "B": "Vertex of right angle", "C": "Midpoint of hypotenuse", "D": "On hypotenuse"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Construct locus of points equidistant from sides of equilateral triangle.", "options": {"A": "Point (center)", "B": "Circle", "C": "Lines", "D": "Triangle"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Locus of midpoints of parallel chords in circle is:", "options": {"A": "Diameter perpendicular to chords", "B": "Chord", "C": "Circle", "D": "Tangent"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Point moves so its distance from (1,0) is half distance from line x=4. Locus:", "options": {"A": "Ellipse", "B": "Circle", "C": "Parabola", "D": "Hyperbola"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Locus of centers of circles of given radius touching given circle is:", "options": {"A": "Two concentric circles", "B": "Circle", "C": "Line", "D": "Point"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Find locus of points 2 units from origin and 3 units from (3,0).", "options": {"A": "0,1,or2 points", "B": "Circle", "C": "Line", "D": "Always 2 points"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Locus of points where ∠APB is constant for fixed A,B (not 90°) is:", "options": {"A": "Arc of circle", "B": "Line", "C": "Complete circle", "D": "Point"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Construct locus of points equidistant from three lines forming triangle.", "options": {"A": "4 points (1 incenter,3 excenters)", "B": "1 point", "C": "Circle", "D": "Lines"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Locus of points P such that PA²+PB²=constant for fixed A,B is:", "options": {"A": "Circle", "B": "Line", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Find locus of points equidistant from (0,0) and line x+y=4.", "options": {"A": "Parabola", "B": "Circle", "C": "Line", "D": "Point"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Locus of centers of circles touching two given circles externally is:", "options": {"A": "Hyperbola", "B": "Ellipse", "C": "Line", "D": "Circle"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Construct locus of points at given distances from two intersecting lines.", "options": {"A": "4 points typically", "B": "Circle", "C": "Line", "D": "Infinite"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Locus of points where ratio of distances from two fixed lines is constant is:", "options": {"A": "Pair of lines", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "Construct locus of points P such that PA+PB=10 cm for fixed A,B with AB=6 cm.", "options": {"A": "Ellipse with foci A,B", "B": "Circle", "C": "Line", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Find locus of points whose distance from (2,3) is twice distance from (-1,-1).", "options": {"A": "Circle", "B": "Line", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Prove that locus of points equidistant from three non-collinear points is circumcenter.", "options": {"A": "By perpendicular bisector property", "B": "By angle bisector", "C": "By median property", "D": "By altitude"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Construct locus of points P such that area ΔPAB=12 cm² for fixed AB=6 cm.", "options": {"A": "Two lines parallel to AB at distance 4 cm", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Find locus of centers of circles touching circle x²+y²=9 and line x=4.", "options": {"A": "Parabola", "B": "Circle", "C": "Ellipse", "D": "Hyperbola"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Construct locus of points equidistant from vertex A of ΔABC and side BC.", "options": {"A": "Parabola with focus A, directrix BC", "B": "Circle", "C": "Line", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Prove that locus of points with constant angle APB is arc of circle.", "options": {"A": "Using inscribed angle theorem", "B": "Using Pythagoras", "C": "Using similar triangles", "D": "Using coordinate geometry"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Find locus of points whose distances from lines 3x+4y=7 and 4x-3y=1 are equal.", "options": {"A": "Two lines: 7x+y=8 and x-7y=6", "B": "Circle", "C": "Point", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Construct locus of points whose sum of distances from sides of equilateral triangle is constant.", "options": {"A": "Line parallel to side", "B": "Circle", "C": "Ellipse", "D": "Hexagon"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Prove that locus of midpoints of chords of circle through fixed point is circle.", "options": {"A": "Using similar triangles and power of point", "B": "Using Pythagoras", "C": "Using coordinate geometry", "D": "Using area formula"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Find locus of points P such that PA²-PB²=24 for A(0,0), B(6,0).", "options": {"A": "Line x=2", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Construct locus of centers of circles touching circle C and line L externally.", "options": {"A": "Parabola", "B": "Circle", "C": "Line", "D": "Point"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Prove that three loci (circles) constructed from three conditions intersect at common point.", "options": {"A": "Using radical center concept", "B": "Using Pythagoras", "C": "Using area", "D": "Using angles"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Find locus of points whose polars with respect to two circles are perpendicular.", "options": {"A": "Circle", "B": "Line", "C": "Point", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Construct locus of points forming triangle with two fixed points having constant area.", "options": {"A": "Two lines parallel to line joining points", "B": "Circle", "C": "Ellipse", "D": "Hyperbola"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Prove that locus of points with constant power wrt two circles is line (radical axis).", "options": {"A": "Using coordinate geometry", "B": "Using Pythagoras", "C": "Using similar triangles", "D": "Using area"}, "correct_answer": "A"},
{"id": 97, "difficulty": "hard", "question": "Find locus of points whose distance from origin is k times distance from line x=a.", "options": {"A": "Circle if k≠1, parabola if k=1", "B": "Always circle", "C": "Always parabola", "D": "Ellipse if k<1"}, "correct_answer": "A"},    {"id": 98, "difficulty": "hard", "question": "Construct locus of points from which tangents to given circle have given length.", "options": {"A": "Concentric circle", "B": "Line", "C": "Point", "D": "Two lines"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Prove that locus of points with constant ratio of distances from two points is circle.", "options": {"A": "Using coordinate geometry/Apollonius", "B": "Using Pythagoras", "C": "Using area", "D": "Using angles"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Find locus of points whose pedal triangle wrt given triangle has constant area.", "options": {"A": "Circle", "B": "Line", "C": "Point", "D": "Parabola"}, "correct_answer": "A"}
  ]
}