Mathematics Conic Section Online Test

Maan AliLast Updated: October 15, 2025

Important Math Conic Section Question and Answer

Total Questions:	50
Time Allowed:	20 Minutes
Total Marks:	50
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Conic Section Practice Test Online With Explanation

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Page 1 of 2

1. The center of the circle is

(b, a)

(a, b)

(0, 0)

2. Equation of circle with center at origin and radius r is

x + y = r

x – y² = r²

x + y² = r²

x – y = r

3. Radius of the circle x² + y² + 12x – 10 y = 0 is

√61

4. Equation of the parabola

y² = 4ax²

x² = 4ay

x = 4ay

y = 4ax

5. The center of the ellipse x²/a² + y²/b² = 1 is

(-1, -1)

(-5, -3)

(1, 1)

(0, 0)

6. The center of the circle x² + y² + 2gx + c = 0 is

(f, g)

(– g, – f)

(g, f)

(– f, – g)

7. Equation of circle with center (h, k) and radius r is

(x + h)² + (y + k)² = r²

(x – h)² + (y + k)² = r²

(x – h)² + (y – k)² = r²

(x – h) + (y – k) = r²

8. Point (x₁, y₁) lies inside the circle x²+y²+2gx+2fy+c= 0 if

x₁² + y₁² + 2gx₁ + 2fy₁ + c = 0

x₁² + y₁² + 2gx₁ + 2fy₁ + c > 0

x₁² + y₁² = 0

x₁² + y₁² + 2gx₁ + 2fy₁ + c < 0

9. For a circle x² + y² = 81, the point (5,6) lies

On the circle

Inside the circle

None of these

Outside the circle

10. If A (0, 0) and (– 1, 0) are ends of the diameter, then the equation fo the circle is

x² + y² – y = 0

x² + y² + x = 0

x² + y² – x = 0

x² + y² + y = 0

11. The extremities of the transverse axis of hyperbola are called its

$Math 20.02$

12. The length of latus – rectum of the ellipse x²/9 + y²/9 = 1 is

4/3

8/3

2/3

1/3

13. If A (0, 0) and (0, 1) are ends of the diameter, then the equation of the circle is

x² + y² + x = 0

x² + y² – x = 0

x² + y² – y = 0

x² + y² + y = 0

14. Focal axis are also known as

Conjugate axis

None of these

Transverse axis

Both a and b

15. Parametric equation of hyperbola are

x = at², y = 2at

x = asec Ø, y = b tan Ø

x = acos Ø, y = b = sin Ø

None of these

16. The parabola y² = 2x passes through

[¼, ¼]

[¼, ½]

(2, 2)

[½, ¼]

17. Equation of tangent to the circle x² + y² = 4 is (2cosθ, 2sinθ) is

xco s θ + y sin θ = √2

xco s θ + y sin θ = 4

xco s θ + y sin θ = 2

xco s θ – y sin θ = 0

18. The line through the focus and perpendicular is directrix is called

Focus

Chord

Directrix

Axis of parabola

19. Circle is special case of

Hyperbola

Ellipse

None of these

Parabola

20. The radius of the circle x²+y²+2gx+2fy+c=0 is

√g²+f²+c

g+f–c

√g²+f²–c

√g²–f²–c

21. The tangents drawn from the point (x₁, y₁) to the circle x² + y² = a² are real and distinct if

x²₁ + y²₁ < a²

x²₁ + y²₁ > a²

x²₁ + y²₁ = a²

x₁ + y₁ < a²

22. Circles (x – 7)² + (y – 9)² = 3 is not concentric to the circle

(x + 7)² + (y + 9)² = √3

(x + 7)² + (y + 9)² = 3√3

(x – 7)² + (y – 9)² = 3

(x + 7)² + (y + 9)² = 9

23. The curves obtain by cutting a (double) right circular cone by a plane are called

Conic sections

Both a and b

None of these

Conics

24. The parabola x² = y passes through

[¼, ½]

[½, ¼]

[½, ½]

(2, 2)

25. The line y = mx + c will be tangent b x²/a² + y²/b² = 1 A > b then

a²+b²m²

a²m²+b²

a²b²+m²

None of these

Page 2 of 2

26. Fixed point from which all points of a circle are equidistant is

Center of hyperbola

Center of the circle

Radius of the circle

Center of ellipse

27. $Math 20.01$

28. Equation of circle with center at origin and radius √5 is

x² + y² = √5

(x – 3)² + y² = 5

x² + y² = 5

x² + y² = 25

29. xx₁ + yy₁ + g(x+x₁) f(y+y₁) + c = 0 represents an equation of

Normal

None of these

Tangent

Slope of tangent

30. If cutting plane is 11 is axis of cone and cuts both of its napes then intersection is

Ellipse

Parabola

None of these

Hyperbola

31. Two circles are said to be concentric circles if they have

Same radius

Same center

Same diameter

Different centers

32. If A (x₁, y₁) and (x₂ – y₂) are ends of the diameter, then the center of the circle is

(x₁+x₂/2 , y₁+y₂/2) = 0

(x₁–x₂/2 , y₁–y₂/2) = 0

(x₁–x₂/2 , y₁+y₂/2) = 0

(x²+y²+x+y) = 0

33. An equation of the form Ax² + By² + Cx + Fy + G = 0 represents a circle if

A = B ≠ 0

None of these

A = 0 or B = 0

A ≠ B

34. The center of the circle (x – 1)² + (y – 3)² = 3 is

(–1, 3)

(– 1, –3)

(1, –3)

(1, 3)

35. Electricity of the ellipse x²/a² + y²/b² = 1 is

None of these

a/c

c/a

36. The size of the circle obtained by cutting the cone by a plane perpendicular to the axis of the cone depends on how near the plane is to the

Space of the cone

Nappe of the cone

Vertex of cone

Axis of the cone

37. The square of the length of the tangent from the point P(x₁y₁) to the circle x² + y² + 2gx + 2fy + c = 0 is

√x²₁ + y²₁ = a²

x²₁ + y²₁ +2gx₁ + 2fy₁ + c

x²₁ + y²₁ > a²

√x²₁ + y²₁ +2gx₁ + 2fy₁ + c

38. Parametric equation of circle x² + y² = r² are

x = r cosh θ, y sin θ

x = r cos θ, y = r sec θ

x = r sec θ, y = r tan θ

x = r cos θ, y = sin θ

39. Parametric equation o ellipse x²/a² + y²/b² = 1

x = asin Ø, y = bcos Ø

x = atan Ø, y = bsec Ø

x = acos Ø, y = bsin Ø

x = asec Ø, y = btan Ø

40. Equation of normal to the circle x² + y² = a² is (aco s θ, a sinθ) is

x cos θ – y sin θ = 0

x sin θ – y cos θ = 0

x cos θ + y sin θ = 0

x sin θ + y cos θ = 0

41. If the intersecting plane is slightly tilted and cuts only one nappe of the cone, the resulting section is

A hyperbola

A parabola

An ellipse

A circle

42. The center of the circle 45x² + 45y² – 60x + 36y + 19 = 0 is

(2/3, –2/5)

(– 2/3, 2/5)

(2/5, 2/3)

(– 2/5, 2/3)

43. Equation of tangent the parabola y² = 4ax at (x + y₁) is

y – y₁ = y₁/2a (x + x₁)

yy₁ =2a (x + x₁)

y – y₁ = 2a/x₁ (x + x₁)

xx₁ = 2a (x + y₁)

44. If the intersecting plane is parallel to the axis of the cone and intersects both of its apes then, the resulting section is

A parabola

An ellipse

A circle

A hyperbola

45. Vertices of x²/a² + y²/b² = 1, a > b are

(± a, 0)

(-a, a)

(a, -a)

(0, ± a)

46. Conic sections or conics are the curves obtained by cutting a come by

Two lines

A plane

A line

A sphere

47. The lines which generate the cone are also known as

Axis of the cone

Rulings

None of these

Vertices

48. The radius of the circle (x – 1)² + (y = 3)² = 3 is

√3

3√3

49. Two tangents from a point p(x₁, y₁) are real and distinct if the point is

Inside the circle

Out side the circle

None of these

One the circle

50. The length of latus – rectum of the ellipse x²/9 + y²/16 = 1

2/9

1/9

9/2

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