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

x² + y² – x = 0

x² + y² + x = 0

x² + y² + y = 0

x² + y² – y = 0

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

x + y² = r²

x – y² = r²

x + y = r

x – y = r

3. 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 cos θ, y = sin θ

x = r sec θ, y = r tan θ

4. $Math 20.01$

5. 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

6. The center of the circle is

(a, b)

(0, 0)

(b, a)

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

A plane

Two lines

A sphere

A line

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

a²+b²m²

a²b²+m²

a²m²+b²

None of these

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

None of these

One the circle

Out side the circle

Inside the circle

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

Axis of the cone

Rulings

None of these

Vertices

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

None of these

a/c

c/a

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

None of these

Conic sections

Both a and b

Conics

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

(x + 7)² + (y + 9)² = 9

(x + 7)² + (y + 9)² = 3√3

(x – 7)² + (y – 9)² = 3

(x + 7)² + (y + 9)² = √3

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

Ellipse

None of these

Parabola

Hyperbola

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

(– g, – f)

(g, f)

(– f, – g)

(f, g)

16. Focal axis are also known as

Transverse axis

Conjugate axis

None of these

Both a and b

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

On the circle

Inside the circle

None of these

Outside the circle

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

x = asin Ø, y = bcos Ø

x = atan Ø, y = bsec Ø

x = asec Ø, y = btan Ø

x = acos Ø, y = bsin Ø

19. The parabola y² = 2x passes through

[¼, ¼]

[¼, ½]

[½, ¼]

(2, 2)

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

A circle

An ellipse

A parabola

A hyperbola

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

x²₁ + y²₁ < a²

x₁ + y₁ < a²

x²₁ + y²₁ = a²

x²₁ + y²₁ > a²

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

Center of ellipse

Center of hyperbola

Center of the circle

Radius of the circle

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

2/3

1/3

8/3

4/3

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

(x – h) + (y – k) = r²

(x – h)² + (y – k)² = r²

(x + h)² + (y + k)² = r²

(x – h)² + (y + k)² = r²

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

A = B ≠ 0

A ≠ B

A = 0 or B = 0

None of these

Page 2 of 2

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

(-1, -1)

(1, 1)

(0, 0)

(-5, -3)

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

x² + y² – y = 0

x² + y² – x = 0

x² + y² + y = 0

x² + y² + x = 0

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

$Math 20.02$

29. Equation of the parabola

x = 4ay

y² = 4ax²

y = 4ax

x² = 4ay

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

(x²+y²+x+y) = 0

(x₁+x₂/2 , y₁+y₂/2) = 0

(x₁–x₂/2 , y₁–y₂/2) = 0

(x₁–x₂/2 , y₁+y₂/2) = 0

31. 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)

32. 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

A hyperbola

An ellipse

A circle

33. 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 +2gx₁ + 2fy₁ + c

√x²₁ + y²₁ = a²

x²₁ + y²₁ > a²

√x²₁ + y²₁ +2gx₁ + 2fy₁ + c

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

y – y₁ = 2a/x₁ (x + x₁)

yy₁ =2a (x + x₁)

y – y₁ = y₁/2a (x + x₁)

xx₁ = 2a (x + y₁)

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

1/9

9/2

2/9

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

None of these

Normal

Tangent

Slope of tangent

37. The parabola x² = y passes through

[¼, ½]

[½, ½]

[½, ¼]

(2, 2)

38. Circle is special case of

None of these

Hyperbola

Ellipse

Parabola

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

(x – 3)² + y² = 5

x² + y² = √5

x² + y² = 5

x² + y² = 25

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

Axis of parabola

Focus

Chord

Directrix

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

(1, 3)

(– 1, –3)

(1, –3)

(–1, 3)

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

√g²+f²–c

g+f–c

√g²–f²–c

√g²+f²+c

43. Parametric equation of hyperbola are

x = asec Ø, y = b tan Ø

x = acos Ø, y = b = sin Ø

x = at², y = 2at

None of these

44. 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 sin θ – y cos θ = 0

x cos θ – y sin θ = 0

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

xco s θ – y sin θ = 0

xco s θ + y sin θ = √2

xco s θ + y sin θ = 4

xco s θ + y sin θ = 2

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

(-a, a)

(0, ± a)

(a, -a)

(± a, 0)

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

3√3

√3

48. 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

Axis of the cone

Vertex of cone

Nappe of the cone

Space of the cone

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

Same center

Same diameter

Different centers

Same radius

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

√61

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