Conics-II

Maths, HSSC-KPK Second Year. This chapter is split into 84 topics and has 1,934 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Angle of rotation that removes the xy term 25 questions
2. Equation of the tangent to a parabola at a point 25 questions
3. Horizontal ellipse centred at the origin: vertices, foci and minor axis 25 questions
4. Ellipse in general form: completing the square 25 questions
5. Condition of tangency of a line to a parabola 25 questions
6. Tangent making a given angle with the x-axis 24 questions
7. Line and hyperbola: nature of intersection 25 questions
8. Rotation of axes: coordinates of a point 24 questions
9. Hyperbola not in standard form (kx squared - my squared = n) 25 questions
10. Translated parabola: vertex, focus and directrix 26 questions
11. Translation of axes: transformed equations (Exercise 8.4 Q1) 20 questions
12. Points of intersection of a line and an ellipse 24 questions
13. Graphing y squared = 4px and x squared = 4py 20 questions
14. Locus problems leading to a parabola or a line 22 questions
15. Ellipse in general form: reducing to standard form 22 questions
16. Points of intersection of a line and a parabola 25 questions
17. Directrix of a parabola from its equation 25 questions
18. Standard forms of the hyperbola and its orientation 22 questions
19. Translation of the parabola: replacing x by x-h and y by y-k 20 questions
20. Translation of axes: coordinates of a point 25 questions
21. Point of contact of a tangent to a parabola 22 questions
22. Derivation of the standard equation of the hyperbola 22 questions
23. Tangent to a parabola with a given slope 22 questions
24. Points of intersection of a line and a hyperbola 24 questions
25. Slopes of the tangent and normal by differentiation 20 questions
26. Equation of the normal to an ellipse at a point 23 questions
27. Tangent and normal to a parabola: concepts and formulas 21 questions
28. Rotation of axes: transformed equations (Exercise 8.4 Q2) 20 questions
29. Parabola from general quadratic form by completing the square 23 questions
30. Equation of the normal to a parabola at a point 25 questions
31. Standard forms of the ellipse and orientation 22 questions
32. Locus: constant difference of distances from two points 22 questions
33. Ellipse: definition and its elements 20 questions
34. Standard forms of the parabola and direction of opening 21 questions
35. Vertical ellipse centred at the origin: vertices, foci and minor axis 25 questions
36. Hyperbola: definition and its elements 20 questions
37. Equation of a translated hyperbola from its elements 20 questions
38. Conic section and eccentricity 27 questions
39. Tangents to a hyperbola parallel or perpendicular to a given line 22 questions
40. Hyperbola in general form: completing the square 25 questions
41. Points on an ellipse and focal distances 21 questions
42. Derivation of the standard equation of the ellipse 22 questions
43. Equation of a translated ellipse from its elements 21 questions
44. Asymptotes of a translated hyperbola 22 questions
45. Parabola definition and its elements 21 questions
46. Tangents to an ellipse with a given slope 24 questions
47. Ellipse not in standard form (kx squared + my squared = n) 25 questions
48. Tangency of lines given in general form to an ellipse (Exercise 8.2 Q5) 21 questions
49. Vertical hyperbola centred at the origin 25 questions
50. Tangents to a hyperbola with a given slope 20 questions
51. Hyperbola in general form: reducing to standard form 20 questions
52. Equation of the normal to a hyperbola at a point 24 questions
53. Tangent and normal to an ellipse: concepts and formulas 21 questions
54. Equation of a parabola passing through a given point 21 questions
55. Condition of tangency of a line to an ellipse 26 questions
56. Eccentricity and the equation of an ellipse (Exercise 8.2 Q4 style) 25 questions
57. Horizontal hyperbola centred at the origin 25 questions
58. Equation of a parabola from focus and directrix (vertex at origin) 24 questions
59. Equation of an ellipse from its elements (centre at the origin) 25 questions
60. General transformation: translation combined with rotation 21 questions
61. Applications of the parabola: cables, antennas and reflectors 20 questions
62. Line and ellipse: nature of intersection 25 questions
63. Comparing the hyperbola with the ellipse 22 questions
64. Equation of the tangent to a hyperbola at a point 24 questions
65. Rectangular hyperbola (Exercise 8.3 Q6) 22 questions
66. Equation of a parabola from vertex and focus or directrix 20 questions
67. Translated ellipse: centre, vertices, foci and minor axis 24 questions
68. Equation of a hyperbola from its elements (centre at the origin) 27 questions
69. Asymptotes of a hyperbola 24 questions
70. Tangency of lines given in general form to a parabola (Exercise 8.1 Q7) 21 questions
71. Eccentricity of an ellipse and the circle as a special case 23 questions
72. Transformation of axes: translation, rotation and general transformation 20 questions
73. Condition of tangency of a line to a hyperbola 26 questions
74. Tangent and normal to a hyperbola: concepts and formulas 20 questions
75. Nature of intersection of a line and a parabola (discriminant) 26 questions
76. Focus of a parabola from its equation 27 questions
77. Tangents parallel or perpendicular to a given line 21 questions
78. Latus rectum of a parabola: length and end points 26 questions
79. Equation of a parabola from focus and directrix (general position) 21 questions
80. Translated hyperbola: centre, vertices, foci and asymptotes 24 questions
81. Derivation of the equation y squared = 4px 21 questions
82. Equation of the tangent to an ellipse at a point 24 questions
83. Tangents to an ellipse parallel or perpendicular to a given line 22 questions
84. Eccentricity of a hyperbola 30 questions