{
  "title": "Loci of Moving Points - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A point moves so that it is always 4 cm from a fixed point O. What is its locus? 🔵", "options": {"A": "Line", "B": "Square", "C": "Circle radius 4 cm", "D": "Two parallel lines"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "A point moves maintaining equal distance from two points A and B. Its locus is ______. ↔️", "options": {"A": "Angle bisector", "B": "Circle", "C": "Perpendicular bisector of AB", "D": "Line through A"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "If a point moves so it's always 3 cm from a fixed line, 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": "A point moves staying 5 units above x-axis. Its locus is ______. 📈", "options": {"A": "x = 5", "B": "y = 5", "C": "x = -5", "D": "y = -5"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "A dog tied to a pole with 2m rope moves. Its locus is ______. 🐕", "options": {"A": "Line", "B": "Circle radius 2 m", "C": "Square", "D": "Rectangle"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "A point moves equidistant from sides of a 60° angle. Its locus is ______. 📐", "options": {"A": "A line at 30°", "B": "Angle bisector", "C": "Perpendicular line", "D": "Circle"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "A point moves such that its distance from origin is 7. Locus equation? 🎯", "options": {"A": "x + y = 7", "B": "x² + y² = 7", "C": "x² + y² = 49", "D": "x = 7, y = 7"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "A point moves keeping equal distance from x-axis and y-axis. Locus is ______. 📍", "options": {"A": "x = y", "B": "x = y and x = -y", "C": "x = 0", "D": "y = 0"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "A ladder slides touching wall and floor. Midpoint's locus is ______. 🪜", "options": {"A": "Straight line", "B": "Circle", "C": "Quarter circle", "D": "Ellipse"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "A point moves so that its x-coordinate is always 4. Locus is ______. 🧭", "options": {"A": "x = 4", "B": "y = 4", "C": "x + y = 4", "D": "x = y = 4"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "A point moves equidistant from two parallel lines 10 cm apart. Locus is ______. ↔️", "options": {"A": "Circle", "B": "Line midway", "C": "Two lines", "D": "Point"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "A point moves so that PA = 3 cm where A fixed. Locus? 🔵", "options": {"A": "Line 3 cm", "B": "Circle radius 3 cm", "C": "Square side 3 cm", "D": "Sphere radius 3 cm"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "A point moves such that it's always 2 cm from a circle of radius 5 cm. Locus? 🔴", "options": {"A": "Circle radius 7 cm", "B": "Two concentric circles radii 3 cm & 7 cm", "C": "Line", "D": "Circle radius 3 cm"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "A point moves so that its distance from (0,2) equals distance from (2,0). Locus is ______. ⚖️", "options": {"A": "x = y", "B": "x + y = 2", "C": "x - y = 0", "D": "x² + y² = 4"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "A point moves along rim of a rolling wheel. Its path is ______. 🌀", "options": {"A": "Circle", "B": "Straight line", "C": "Cycloid", "D": "Ellipse"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "A point moves so it's equidistant from sides of a square. Locus inside is ______. ⬜", "options": {"A": "Circle", "B": "Point", "C": "Square", "D": "Two lines"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "A point moves such that sum of distances from two fixed points is 10 cm (points 6 cm apart). Locus? ➕", "options": {"A": "Circle", "B": "Ellipse", "C": "Line", "D": "Parabola"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "A point moves so that its distance from line y = 3 equals distance from origin. Locus? 📍", "options": {"A": "Line", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "A point moves so that PA ⟂ PB for fixed A, B. Locus? 📐", "options": {"A": "Line", "B": "Circle with AB diameter", "C": "Ellipse", "D": "Parabola"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "A point moves so that PA = 2PB, A(0,0), B(4,0). Locus? ⚖️", "options": {"A": "Line", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "B"},
    {"id": 21, "difficulty": "medium", "question": "A point moves so that its distance from (1,0) is equal to distance from line x = -1. Locus? 📍", "options": {"A": "Parabola y² = 4x", "B": "Circle", "C": "Ellipse", "D": "Line"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "A point P moves such that PA² + PB² = AB² (A,B fixed). Locus? 🧠", "options": {"A": "Circle with AB diameter", "B": "Perpendicular bisector", "C": "Line ⟂ AB", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "A point moves so that difference of distances from (3,0) and (-3,0) is 4. Locus? ➖", "options": {"A": "Ellipse", "B": "Hyperbola", "C": "Circle", "D": "Parabola"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "A point moves so that it is equidistant from three non-collinear points. Locus? 🔺", "options": {"A": "Point", "B": "Line", "C": "Circle", "D": "Triangle"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "A point moves so that area of triangle with vertices (0,0), (4,0), and P is 10 sq units. Locus? 📊", "options": {"A": "Line y = 5", "B": "Line y = ±5", "C": "Line x = 5", "D": "Circle"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "A point moves so that its distance from (2,3) is twice distance from (-1,-1). Locus? 📏", "options": {"A": "Circle", "B": "Line", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "A point P moves so that slope of AP = 2 × slope of BP, A(1,2), B(3,4). Locus? 📈", "options": {"A": "Line", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "A point moves such that sum of its distances from coordinate axes is 5. Locus? ➕", "options": {"A": "Line x + y = 5", "B": "Square", "C": "Four line segments", "D": "Circle"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "A point moves so that PA × PB = 25, A(0,0), B(6,0). Locus? ✖️", "options": {"A": "Circle", "B": "Line", "C": "Ellipse", "D": "Hyperbola"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "A point moves so that it's always at distance 3 from line x + y = 1. Locus? 📏", "options": {"A": "Two lines x+y=1±3√2", "B": "Circle", "C": "One line", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "A point moves so that its polar angle equals its radius (r = θ). Locus? 📐", "options": {"A": "Spiral", "B": "Circle", "C": "Line", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "A point moves so that its distance from origin is equal to distance from line x = a. Locus? 📍", "options": {"A": "Parabola", "B": "Circle", "C": "Two lines", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "A point moves so that it divides line joining (0,0) and (4,4) in ratio 1:2. Locus? 🔢", "options": {"A": "Line", "B": "Circle", "C": "Parabola", "D": "Point"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "A point moves so that PA² - PB² = 12, A(1,1), B(4,5). Locus? ⚖️", "options": {"A": "Line", "B": "Circle", "C": "Ellipse", "D": "Hyperbola"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "A point moves so that it is always midpoint of line joining (a,0) and (0,b) where a,b vary but a+b=10. Locus? 📏", "options": {"A": "Line x + y = 5", "B": "Circle", "C": "Ellipse", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "A point moves so that its projection on x-axis is 3. Locus? 📍", "options": {"A": "x = 3", "B": "y = 3", "C": "Line parallel to y-axis", "D": "Circle"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "A point moves so that ratio of distances from lines x = 0 and y = 0 is 2:1. Locus? ⚖️", "options": {"A": "Two lines", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "A point moves so that it is equidistant from (1,1) and line x + y + 2 = 0. Locus? 📏", "options": {"A": "Parabola", "B": "Circle", "C": "Line", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "A point moves so that its distance from (0,a) is equal to its distance from line y = -a. Locus? 📍", "options": {"A": "Parabola", "B": "Circle", "C": "Ellipse", "D": "Line"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "A point moves so that it's always at distance 1 from line 3x + 4y = 5. Locus? 📏", "options": {"A": "Two lines", "B": "Circle", "C": "One line", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "A point moves so that sum of squares of distances from vertices of equilateral triangle is constant. Locus? 🔺", "options": {"A": "Circle", "B": "Point", "C": "Line", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "A point moves so that PA² + PB² + PC² = k, A,B,C fixed. Locus? 🧮", "options": {"A": "Circle", "B": "Point", "C": "Line", "D": "Sphere"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "A point moves so that its pedal triangle w.r.t. fixed triangle has constant area. Locus? 📐", "options": {"A": "Circle", "B": "Line", "C": "Ellipse", "D": "Hyperbola"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "A point moves so that its polar w.r.t. circle x²+y²=a² touches parabola y²=4ax. Locus? 🔵", "options": {"A": "Line", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "hard", "question": "A point moves so that its distances from four sides of a square are in arithmetic progression. Locus? ⬜", "options": {"A": "Line", "B": "Circle", "C": "Point", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "A point moves so that chord of contact w.r.t. circle x²+y²=r² subtends right angle at center. Locus? 📐", "options": {"A": "Circle", "B": "Line", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "A point moves so that its polar lines w.r.t. two fixed circles are perpendicular. Locus? 🔄", "options": {"A": "Circle", "B": "Line", "C": "Orthogonal circle", "D": "Ellipse"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "A point moves so that its harmonic conjugate w.r.t. two fixed points lies on fixed line. Locus? 📏", "options": {"A": "Circle", "B": "Line", "C": "Ellipse", "D": "Hyperbola"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "A point moves so that its distance from a fixed point is proportional to its distance from a fixed line (ratio ≠1). Locus? 📍", "options": {"A": "Circle", "B": "Ellipse", "C": "Parabola", "D": "Hyperbola"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "A point moves so that tangents from it to two fixed circles have equal lengths. Locus? 🔄", "options": {"A": "Line", "B": "Circle", "C": "Radical axis", "D": "Ellipse"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "hard", "question": "A point moves so that its reflections in two fixed lines are always collinear with a fixed point. Locus? 📐", "options": {"A": "Line", "B": "Circle", "C": "Ellipse", "D": "Hyperbola"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "hard", "question": "A point moves so that its normal to parabola y²=4ax is tangent to circle x²+y²=a². Locus? 🔵", "options": {"A": "Line", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "hard", "question": "A point moves so that its complex representation z satisfies |z-a|+|z-b|=c. Locus? 🔢", "options": {"A": "Ellipse", "B": "Hyperbola", "C": "Circle", "D": "Line segment"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "A point moves so that its distance from (0,0) is equal to its distance from line x+y=2√2. Locus? 📏", "options": {"A": "Parabola", "B": "Circle", "C": "Two lines", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "A point moves so that its trilinear coordinates satisfy α+β+γ=0 w.r.t. fixed triangle. Locus? 🔺", "options": {"A": "Line at infinity", "B": "Circle", "C": "Ellipse", "D": "Conic"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "A point moves so that its Simson line w.r.t. a fixed triangle has fixed direction. Locus? 📐", "options": {"A": "Circle", "B": "Line", "C": "Ellipse", "D": "Parabola"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "A point moves so that its pedal circle w.r.t. fixed triangle passes through fixed point. Locus? 🔄", "options": {"A": "Line", "B": "Circle", "C": "Ellipse", "D": "Conic"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "A point moves so that its isogonal conjugate lies on fixed line. Locus? 📏", "options": {"A": "Conic through vertices", "B": "Circle", "C": "Line", "D": "Ellipse"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "A point moves so that its orthocenter relative to fixed triangle is fixed point. Locus? 🔺", "options": {"A": "Circle", "B": "Line", "C": "Ellipse", "D": "Conic"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "A point moves so that its distance from vertex A of triangle ABC is proportional to its distance from side BC. Locus? 📐", "options": {"A": "Circle", "B": "Line", "C": "Conic", "D": "Ellipse"}, "correct_answer": "C"}
  ]
}