Conic Section | Circle - MCQs | National Book Foundation

Conic Section – Circle (Exercise 7.1, Exercise 7.2, Exercise 7.3) Conic Section – Circle MCQs from National Book Foundation provides a focused collection of multiple-choice questions to help students understand the key concepts of circles in analytical geometry. This resource covers important topics such as equations of a circle, radius, center, tangents, chords, and related properties. It is ideal for students preparing for board exams, entry tests, and competitive exams, offering practice-based learning to strengthen problem-solving skills and conceptual clarity.

Topic: Circle
 
March 28, 2026

Name
1. 
The set of all the points in the plane that are equally distant from a fixed point is called a:

2. 
If a plane passes through the vertex of the cone, then the intersection is:

3. 
A cone is generated by all lines through a fixed point and the circumference of;

4. 
The fixed point which lies on the axis of the cone is called its:

5. 
The surface generated by lines, consistent of two parts, called:

6. 
The lines that form the cone are called its:

7. 
If the cone is cut by a plane perpendicular to the axis of the cone, then the section is a;

8. 
The vertex of the cone are also called:

9. 
The generators of a cone are also called:

10. 
If the cutting plane is slightly tilted and cuts only one nappe of the cone, the resulting section is:

11. 
If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve of intersection is:

12. 
If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is:

13. 
The familiar plane curves namely circles, ellipse, parabola and hyperbola are obtained from:

14. 
To study conics, Pappus used the method of:

15. 
Apollonius was a:

16. 
The centre and radius of the circle $5x^{2}+5y^{2}+24x+24y+10=0$ are:

17. 
The equation $x^{2}+y^{2}+2gx+2fy+c=0$ represents:

18. 
A second degree equation in which coefficients of $x^{2}$ and $y^{2}$ are equal and there is no product term $xy$ represents:

19. 
The equation of the circle whose centre is $(-3,5)$ and having radius $7$ is:

20. 
If three non-collinear points through which a circle passes are known, then we can find the:

21. 
If centre of the circle is the origin, then equation of the circle is:

22. 
The equation $x^{2}+y^{2}+2gx+2fy+c=0$ degenerates to a point circle if:

23. 
The equation of the circle with centre at $(5,-2)$ and radius $4$ is:

24. 
The centre and radius of the circle $4x^{2}+4y^{2}-8x+12y-25=0$ are:

25. 
The radius of the circle $x^{2}+y^{2}-6x+4y+13=0$ is:

26. 
The centre and radius of the circle $5x^{2}+5y^{2}+14x+12y-10=0$ are:

27. 
Equation of the circle having the join of $A(x_1,y_1)$ and $B(x_2,y_2)$ as diameter is:

28. 
The area of the circle centred at $(1,2)$ and passing through $(4,6)$ is:

29. 
The equation of the circle which passes through $(4,5)$ and whose centre is $(2,2)$ is:

30. 
The equation $ax^{2}+by^{2}+2hxy+2gx+2fy+c=0$ represents a circle iff:

31. 
Equation of the circle passing through $A(3,-1)$, $B(0,1)$ and having centre $4x-3y-3=0$ is:

32. 
The general equation of a circle $x^{2}+y^{2}+2gx+2fy+c=0$ contains:

33. 
Parametric equations of circle $x^{2}+y^{2}=r^{2}$ are:

34. 
The radius of the circle $2x^{2}+2y^{2}-4x+12y+11=0$ is:

35. 
The equation $x^{2}+y^{2}+2gx+2fy+c=0$ represents a circle whose centre is:

36. 
The equation $x^{2}+y^{2}+2gx+2fy+c=0$ represents a circle whose radius is:

37. 
If a circle passes through the points $(2,-1)$, $(2,3)$, $(4,-1)$ then its radius is:

38. 
The centre of the circle $ax^{2}+ay^{2}=bx+cy$ is:

39. 
The radius of the circle $7x^{2}+7y^{2}-4x-y-3=0$ is:

40. 
The radius of the circle \[ x^2 + y^2 + 8x - 2y - 8 = 0 \] is:

41. 
The centre and radius of the circle \[ 2x^2 + 2y^2 - 3x + 2y + 1 = 0 \] are:

42. 
The centre and radius of the circle \[ 3x^2 + 3y^2 + 6x - 3y - 2 = 0 \] are:

43. 
The equation of the circle with centre $(2,7)$ passing through $(-3,-5)$ is:

44. 
If the line joining $(2,1)$ to $(6,5)$ is a diameter of the circle, then equation of the circle is:

45. 
If the equation $(x-a)^2 + (y-b)^2 = c^2$ represents a circle, then:

46. 
The circles $x^2 + y^2 - 6x + 5 = 0$ and $x^2 + y^2 - 8x + 7 = 0$ touch each other, the point of contact is:

47. 
The point of contact of the circles \[ x^2 + y^2 - 6x - 6y + 10 = 0 \quad \text{and} \quad x^2 + y^2 = 2 \] is:

48. 
The circles $x^2 + y^2 - 4x + 6y + 8 = 0$ and $x^2 + y^2 - 10x - 6y + 14 = 0$:

49. 
If the two circles $x^2 + y^2 + 2gx + 2fy = 0$ and $x^2 + y^2 + 2g'x + 2f'y = 0$ touch each other, then:

50. 
Circles $x^2 + y^2 - 2x - y = 0$ and $x^2 + y^2 - 8y - 4 = 0$:

51. 
Circles $x^2 + y^2 - 10x + 4y - 20 = 0$ and $x^2 + y^2 + 14x - 6y + 22 = 0$:

52. 
Points of intersection of $x^2 + y^2 = 25$ and $x^2 + y^2 - 8x + 7 = 0$ are:

53. 
Two circles $x^2 + y^2 - 4x - 6y - 8 = 0$ and $x^2 + y^2 - 2x - 3 = 0$:

54. 
Circles $x^2 + y^2 - 2x - 4y = 0$ and $x^2 + y^2 - 8y - 4 = 0$:

55. 
Two circles $x^2 + y^2 + 2x - 2y - 7 = 0$ and $x^2 + y^2 - 6x + 4y - 9 = 0$:

56. 
Two circles $x^2 + y^2 + 2x - 8 = 0$ and $x^2 + y^2 - 6x + 6y - 46 = 0$:

57. 
Equation of the circle which passes through $(3,-6)$ and touches both the axes is:

58. 
The equation of the circle which touches both axes and whose radius is $a$, is:

59. 
Circle $x^2 + y^2 + 4x - 4y + 4 = 0$ touches:

60. 
Equation of a circle which passes through $(3,6)$ and touches the axis is:

61. 
This circle represents:

62. 
If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ touches $x$-axis, then:

63. 
If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ touches both $x$-axis and $y$-axis, then coordinates of the centre is:

64. 
If the circle $(x-h)^2 + (y-k)^2 = r^2$ touches $y$-axis then equation of the circle is:

65. 
The equation of the circle $(x-h)^2 + (y-k)^2 = r^2$, passing through the origin having centre on $x$-axis is:

66. 
The equation of circle passing through $(1,-2)$ and $(3,-4)$ and touches $x$-axis is:

67. 
If $(x_1,y_1)$ and $(x_2,y_2)$ are ends of the diameter, then the centre of the circle is:

68. 
The equation of the circle, if $(1,2)$ and $(2,3)$ are the ends of the diameter, is:

69. 
If the circle $x^2 + y^2 + 2x - 2y + c = 0$ passes through $(1,-1)$, then $c =?$:

70. 
The points of intersection of the line $y = 2x - 3$ and the circle \[ x^2 + y^2 - 3x + 2y - 3 = 0 \] are:

71. 
One of the points of intersection of the line \[ 2x - y + 1 = 0 \] and circle \[ x^2 + y^2 = 2 \] is:

72. 
The equation of the circle containing the points $(1,-2)$ and $(4,-3)$ and having the centre on the straight line $3x + 4y = 7$ is:

73. 
The line \[ 4x + 3y + k = 0 \] will touch the circle \[ 2x^2 + 2y^2 = 5x \] if $k =$:

74. 
The coordinates of the point of intersection of \[ x^2 + y^2 = 25 \] and \[ 3x + y = 5 \] are:

75. 
Equation of the tangent to the circle \[ x^2 + y^2 + 2gx + 2fy + c = 0 \] at $(x_1,y_1)$ is:

76. 
The slope of the tangent of the circle \[ x^2 + y^2 = 25 \] at $(4,3)$ is:

77. 
The slope of the tangent at $(5\cos\theta,5\sin\theta)$ of the circle \[ x^2 + y^2 = 25 \] is:

78. 
The slope of the normal at $\left(1,\frac{10}{3}\right)$ to the circle \[ 3x^2 + 4y^2 - 16x + 24y - 117 = 0 \] is:

79. 
The slope of the normal at $(4,3)$ to the circle \[ x^2 + y^2 = 25 \] is:

80. 
The points on the circle \[ x^2 + y^2 - 4x + 6y + 9 = 0 \] with ordinate $-2$ are:

81. 
The slope of the tangent at $(x_1,y_1)$ to the circle \[ x^2 + y^2 + 2gx + 2fy + c = 0 \] is:

82. 
The equation of the normal at $(x_1,y_1)$ to the circle \[ x^2 + y^2 + 2gx + 2fy + c = 0 \] is:

83. 
The equation of the tangent to the circle \[ x^2 + y^2 = 2 \] parallel to the line $x - 2y = 1$ is:

84. 
The equations of the tangents to the circle \[ x^2 + y^2 = 2 \] perpendicular to the line $3x + 2y = 6$ are:

85. 
Equation of tangent to the circle \[ x^2 + y^2 = 7 \] at $(\sqrt{7}\cos\theta, \sqrt{7}\sin\theta)$ is:

86. 
Equations of tangents to the circle \[ x^2 + y^2 - 6x + 4y = 12 \] parallel to $4x + 3y + 5 = 0$ are:

87. 
Equation of the normal to the circle \[ x^2 + y^2 - 3x - 6y - 10 = 0 \] at the point $(-3,4)$ is:

88. 
Equation of tangent to the circle \[ x^2 + y^2 = 5 \] at $(\sqrt{5}\cos\theta, \sqrt{5}\sin\theta)$ is:

89. 
Equation of normal to the circle \[ x^2 + y^2 = a^2 \] at $(a\cos\theta, a\sin\theta)$ is:

90. 
The slope of the normal at $(5\cos\theta,5\sin\theta)$ to the circle \[ x^2 + y^2 = 25 \] is:

1 out of 90

Entry Test Preparation
Entry Test Preparation
Exit mobile version