{
  "title": "Definition of Locus - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What does 'locus' mean in geometry? 📍", "options": {"A": "A fixed point", "B": "Set of all points satisfying a condition", "C": "A line segment", "D": "A type of angle"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "The locus of points at a constant distance from a fixed point is a ______. 🔵", "options": {"A": "line", "B": "ray", "C": "circle", "D": "triangle"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "If a point moves so that it's always 5 cm from line L, its locus is ______. 📏", "options": {"A": "one line", "B": "two parallel lines", "C": "a circle", "D": "a square"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Locus of points equidistant from two fixed points is the ______. ↔️", "options": {"A": "angle bisector", "B": "perpendicular bisector", "C": "median", "D": "altitude"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "A locus can be a ______. ✅", "options": {"A": "point", "B": "line", "C": "curve", "D": "all of these"}, "correct_answer": "D"},
    {"id": 6, "difficulty": "easy", "question": "The locus of centers of all circles passing through two given points is ______. 🔄", "options": {"A": "a circle", "B": "a line", "C": "perpendicular bisector of the points", "D": "an arc"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "If a point's distance from the x-axis equals its distance from the y-axis, its locus is ______. 📍", "options": {"A": "x = y and x = -y", "B": "x = 0", "C": "y = 0", "D": "x² + y² = 1"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Locus of a point moving in a plane such that its distance from (0,0) is 4 units is ______. 🎯", "options": {"A": "line x=4", "B": "circle radius 4", "C": "square", "D": "ellipse"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "What is the locus of a point equidistant from two intersecting lines? ✖️", "options": {"A": "circle", "B": "two lines", "C": "angle bisectors", "D": "perpendicular line"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "A point remains at equal distance from sides AB and AC of triangle ABC. Its locus is ______. 📐", "options": {"A": "median from A", "B": "angle bisector of ∠A", "C": "perpendicular bisector of BC", "D": "altitude from A"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Locus of all points at a distance of 2 cm from a given point P is a ______. ⭕", "options": {"A": "line of length 2 cm", "B": "circle radius 2 cm", "C": "square side 2 cm", "D": "sphere"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If a point moves so that it's always 3 units above the x-axis, its locus is ______. 📈", "options": {"A": "y = 3", "B": "x = 3", "C": "y = -3", "D": "x = -3"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "What is the locus of midpoints of all chords of length 6 cm in a given circle? 🎵", "options": {"A": "a line", "B": "a circle concentric with given circle", "C": "a point", "D": "an ellipse"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Locus of points at a constant distance from a fixed line is ______ lines. ↔️", "options": {"A": "one", "B": "two parallel", "C": "three", "D": "infinite"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "A point's distance from point A is always equal to its distance from point B. Locus is ______. ⚖️", "options": {"A": "circle with diameter AB", "B": "perpendicular bisector of AB", "C": "line through A", "D": "line through B"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Locus of points equidistant from two parallel lines is ______. 📏", "options": {"A": "a line midway between them", "B": "a circle", "C": "two lines", "D": "a point"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "If a point moves keeping equal distance from sides of a right angle, its locus is ______. 📐", "options": {"A": "a line at 45°", "B": "a circle", "C": "a parabola", "D": "the hypotenuse"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Locus of a point whose x-coordinate is always 5 is ______. 🧭", "options": {"A": "line x = 5", "B": "line y = 5", "C": "circle radius 5", "D": "point (5,0)"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "A point moves so that its distance from origin is always 7. Locus is ______. 🔵", "options": {"A": "x² + y² = 7", "B": "x² + y² = 49", "C": "x + y = 7", "D": "x = 7, y = 7"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Locus of a point P such that PA = 3 cm, where A is fixed, is a ______. 📍", "options": {"A": "line 3 cm long", "B": "circle with center A, radius 3 cm", "C": "square side 3 cm", "D": "sphere"}, "correct_answer": "B"},
    {"id": 21, "difficulty": "medium", "question": "Find the locus of a point whose distance from (2,3) is twice its distance from (-1, -1). 📐", "options": {"A": "circle", "B": "line", "C": "parabola", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Locus of points P such that PA² + PB² = AB² (A,B fixed) is ______. 🧠", "options": {"A": "circle with AB as diameter", "B": "line ⟂ AB", "C": "line ∥ AB", "D": "perpendicular bisector"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "If a point's distance from the line x = 4 is equal to its distance from the point (2,2), the locus is ______. 📍", "options": {"A": "line", "B": "circle", "C": "parabola", "D": "ellipse"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Locus of point P such that area of ∆PAB is constant (A,B fixed) is ______. 📊", "options": {"A": "line parallel to AB", "B": "circle with diameter AB", "C": "perpendicular bisector", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "A point moves so that sum of its distances from two fixed points is constant. Locus is ______. ➕", "options": {"A": "circle", "B": "ellipse", "C": "hyperbola", "D": "parabola"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Locus of centers of circles touching two intersecting lines is ______. 🔵", "options": {"A": "angle bisectors", "B": "perpendicular bisector", "C": "circle", "D": "line parallel to one"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Point P moves such that PA = 2PB, with A(0,0), B(3,0). Locus is ______. 📐", "options": {"A": "line", "B": "circle", "C": "parabola", "D": "ellipse"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Locus of points equidistant from three non-collinear points is ______. 🔺", "options": {"A": "a point", "B": "a line", "C": "a circle", "D": "none"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "If a point's distance from (1,0) is equal to its distance from the line x = -1, the locus is ______. 📍", "options": {"A": "line", "B": "circle", "C": "parabola", "D": "ellipse"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "Locus of point P such that ∠APB = 90° (A,B fixed) is ______. 📐", "options": {"A": "line", "B": "circle with AB as diameter", "C": "ellipse", "D": "hyperbola"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "A point's distance from the y-axis is twice its distance from the x-axis. Locus is ______. 📊", "options": {"A": "x = 2y", "B": "|x| = 2|y|", "C": "y = 2x", "D": "|y| = 2|x|"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "Locus of point P such that PA² - PB² = constant (A,B fixed) is ______. ⚖️", "options": {"A": "line ⟂ AB", "B": "line ∥ AB", "C": "circle", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "If a point moves so that its distance from point (0,2) is equal to its distance from line y = -2, locus is ______. 📍", "options": {"A": "line", "B": "circle", "C": "parabola", "D": "ellipse"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Locus of centers of circles of radius 3 touching a given line L is ______. 🔵", "options": {"A": "a line parallel to L at distance 3", "B": "two lines parallel to L at distance 3", "C": "a circle", "D": "a line perpendicular to L"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Point P moves so that PA + PB = 10, with A(-3,0), B(3,0). Locus is ______. ➕", "options": {"A": "circle", "B": "ellipse", "C": "line", "D": "hyperbola"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Locus of points P such that PA/PB = k (k ≠ 1) is a ______. ⚖️", "options": {"A": "line", "B": "circle", "C": "parabola", "D": "ellipse"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "If a point is equidistant from sides of an equilateral triangle, its locus inside triangle is ______. 🔺", "options": {"A": "a circle", "B": "a point", "C": "three lines", "D": "a line"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Locus of a point P such that the slope of PA is twice slope of PB (A,B fixed) is ______. 📈", "options": {"A": "line", "B": "circle", "C": "parabola", "D": "hyperbola"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "A point moves so that its distance from (a,0) and (-a,0) differs by 2a. Locus is ______. ➖", "options": {"A": "line", "B": "circle", "C": "hyperbola", "D": "parabola"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "Locus of midpoints of chords of circle x² + y² = 25 passing through (1,2) is ______. 🎵", "options": {"A": "line", "B": "circle", "C": "point", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "Find locus of P such that PA² + PB² + PC² is constant (A,B,C fixed). 🧠", "options": {"A": "circle", "B": "point", "C": "line", "D": "sphere"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Locus of points P such that projection of AP on line L equals projection of BP on L (A,B fixed, L given) is ______. 📍", "options": {"A": "line ⟂ L", "B": "line ∥ L", "C": "circle", "D": "ellipse"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "P moves so that sum of squares of distances from vertices of square is constant. Locus is ______. ⬜", "options": {"A": "circle", "B": "square", "C": "point", "D": "line"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "Locus of point P such that PA × PB = constant (A,B fixed) is ______. ✖️", "options": {"A": "circle", "B": "line", "C": "lemniscate", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "A point moves so that its distance from point (0,a) is equal to its distance from line y = -a. Locus is ______. 📍", "options": {"A": "parabola y = x²/4a", "B": "circle", "C": "ellipse", "D": "line"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Locus of point P such that ∠APB = θ (constant, 0°<θ<180°) is ______. 📐", "options": {"A": "arc of a circle", "B": "full circle", "C": "line", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "If a point's distance from (3,4) is half its distance from line x = 6, locus is ______. 📍", "options": {"A": "circle", "B": "ellipse", "C": "parabola", "D": "hyperbola"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "Locus of point P such that PA = PB = PC (A,B,C non-collinear) is ______. 🔺", "options": {"A": "a point", "B": "a line", "C": "a circle", "D": "none"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "P moves so that PA² - PB² = PC² - PD² (A,B,C,D rectangle vertices). Locus is ______. ⬜", "options": {"A": "line", "B": "circle", "C": "point", "D": "plane"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "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": 51, "difficulty": "hard", "question": "A point moves so that its polar coordinates satisfy r = aθ (a constant). Locus is ______. 📏", "options": {"A": "circle", "B": "spiral", "C": "line", "D": "parabola"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "hard", "question": "Locus of point P such that area(∆PAB)/area(∆PCD) = constant (A,B,C,D fixed) is ______. 📊", "options": {"A": "line", "B": "circle", "C": "hyperbola", "D": "ellipse"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "If a point's distance from origin is proportional to its distance from line x = a, locus is ______. 📍", "options": {"A": "circle", "B": "line", "C": "parabola", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Locus of point P such that tan(∠APB) = constant (A,B fixed) is ______. 📐", "options": {"A": "circle", "B": "line", "C": "parabola", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "P moves so that PA + PB = PC + PD (A,B,C,D square vertices). Locus is ______. ⬜", "options": {"A": "line", "B": "circle", "C": "square", "D": "point"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Locus of centers of mass of all triangles with vertices on three given parallel lines is ______. 📏", "options": {"A": "a line", "B": "a circle", "C": "a point", "D": "plane"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "If a point's distance from line x + y = 1 equals its distance from line x - y = 1, locus is ______. 📍", "options": {"A": "lines x=1 and y=1", "B": "lines x=0 and y=0", "C": "lines x=1 and y=0", "D": "lines x=0 and y=1"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "Locus of point P such that harmonic mean of PA and PB is constant (A,B fixed) is ______. 🧮", "options": {"A": "circle", "B": "line", "C": "ellipse", "D": "hyperbola"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "A point moves so that its coordinates satisfy x³ + y³ = 3axy. Locus is ______. 📈", "options": {"A": "circle", "B": "line", "C": "folium of Descartes", "D": "ellipse"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "hard", "question": "Locus of points whose sum of distances to sides of a triangle is constant is ______. 🔺", "options": {"A": "line", "B": "circle", "C": "ellipse", "D": "hyperbola"}, "correct_answer": "A"}
  ]
}