Home/Mathematics/Mathematics Conic Section Online Test

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.
Test Helpful For:	ECAT Entry Test Mathematics Online Test Interview Questions about Mathematics All Universities Entrance Test Recruitments Tests

Math Conic Section Practice Test Online With Explanation

Please wait...

Page 1 of 2

1. Circle is special case of

Hyperbola

None of these

Parabola

Ellipse

2. The parabola x² = y passes through

[¼, ½]

[½, ½]

(2, 2)

[½, ¼]

3. 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 + y = 0

x² + y² + x = 0

x² + y² – x = 0

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

x² + y² = 5

x² + y² = 25

x² + y² = √5

(x – 3)² + y² = 5

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

A plane

Two lines

A line

A sphere

6. 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

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

(– 2/3, 2/5)

(– 2/5, 2/3)

(2/5, 2/3)

(2/3, –2/5)

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

x = atan Ø, y = bsec Ø

x = asec Ø, y = btan Ø

x = asin Ø, y = bcos Ø

x = acos Ø, y = bsin Ø

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

x – y² = r²

x + y² = r²

x – y = r

x + y = r

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

A parabola

A hyperbola

A circle

An ellipse

11.

12. 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

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

Axis of the cone

Rulings

None of these

Vertices

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

Ellipse

Parabola

Hyperbola

None of these

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

(0, ± a)

(-a, a)

(± a, 0)

(a, -a)

16. The center of the circle is

(b, a)

(0, 0)

(a, b)

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

√61

18. Equation of the parabola

y = 4ax

y² = 4ax²

x² = 4ay

x = 4ay

19. 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

20. 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 – y = 0

x² + y² + x = 0

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

2/3

1/3

8/3

4/3

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

x cos θ – y sin θ = 0

x cos θ + y sin θ = 0

x sin θ + y cos θ = 0

x sin θ – y cos θ = 0

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

xx₁ = 2a (x + y₁)

yy₁ =2a (x + x₁)

y – y₁ = y₁/2a (x + x₁)

y – y₁ = 2a/x₁ (x + x₁)

24. 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 +2gx₁ + 2fy₁ + c

x²₁ + y²₁ > a²

25. Parametric equation of hyperbola are

x = acos Ø, y = b = sin Ø

None of these

x = asec Ø, y = b tan Ø

x = at², y = 2at

Page 2 of 2

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

A ≠ B

None of these

A = B ≠ 0

A = 0 or B = 0

27. 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

(x²+y²+x+y) = 0

(x₁–x₂/2 , y₁–y₂/2) = 0

(x₁+x₂/2 , y₁+y₂/2) = 0

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

Center of the circle

Radius of the circle

Center of hyperbola

Center of ellipse

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

x = r cos θ, y = r sec θ

x = r sec θ, y = r tan θ

x = r cosh θ, y sin θ

x = r cos θ, y = sin θ

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

(– f, – g)

(f, g)

(– g, – f)

(g, f)

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

A hyperbola

A circle

A parabola

An ellipse

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

Chord

Directrix

Focus

Axis of parabola

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

9/2

1/9

2/9

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

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

Tangent

Slope of tangent

None of these

Normal

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

Same diameter

Same center

Same radius

Different centers

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

(1, 3)

(–1, 3)

(– 1, –3)

(1, –3)

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

3√3

√3

39. 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

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

√g²+f²+c

√g²+f²–c

√g²–f²–c

g+f–c

41. 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

Space of the cone

Nappe of the cone

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

(-5, -3)

(-1, -1)

(0, 0)

(1, 1)

43. Focal axis are also known as

None of these

Transverse axis

Both a and b

Conjugate axis

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

On the circle

Outside the circle

None of these

Inside the circle

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

Inside the circle

None of these

Out side the circle

One the circle

46. 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

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

a/c

c/a

None of these

48. The parabola y² = 2x passes through

[¼, ¼]

[½, ¼]

(2, 2)

[¼, ½]

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

a²+b²m²

None of these

a²b²+m²

a²m²+b²

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

Conics

Both a and b

Conic sections

None of these

You Can Learn and Gain more Knowledge through our Online Quiz and Testing system Just Search your desired Preparation subject at Gotest.

Mathematics Linear Inequalities and Linear Programming Test ...
Mathematics Inverse Trigonometric Functions Online Test
Mathematics Application of Trigonometry Online Test
Mathematics Solution of Trigonometric Functions Online Test
Mathematics Functions and Limits Online Test
Mathematics Induction and Binomial Theorem Online Test
Mathematics Differentiation Online Test
Mathematics Integration Online Test
Mathematics Permutations Combinations and Probability Online...
Mathematics Introduction to Analytic Geometry Online Test

Maan AliLast Updated: October 15, 2025

Mathematics Conic Section Online Test

Important Math Conic Section Question and Answer

Math Conic Section Practice Test Online With Explanation

Related Posts

Maan Ali

Leave a Reply Cancel reply