Home/ECAT/ECAT Mathematics Conic Section Online Test

ECAT Mathematics Conic Section Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Conic Section

ECAT Math Conic Section Chapter Online Test

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

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1. 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 +2gx₁ + 2fy₁ + c

√x²₁ + y²₁ = a²

x²₁ + y²₁ > a²

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

Vertices

Rulings

Axis of the cone

None of these

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

A plane

Two lines

A line

A sphere

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

None of these

Both a and b

Conics

Conic sections

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

(-1, -1)

(-5, -3)

(1, 1)

(0, 0)

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

A hyperbola

A circle

An ellipse

A parabola

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

A = B ≠ 0

A = 0 or B = 0

A ≠ B

None of these

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

Inside the circle

Out side the circle

One the circle

None of these

9. 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

10. Circle is special case of

Parabola

Hyperbola

Ellipse

None of these

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

Focus

Axis of parabola

Chord

Directrix

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

c/a

a/c

None of these

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

a²b²+m²

a²+b²m²

a²m²+b²

None of these

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

1/3

2/3

8/3

4/3

15. 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

(x – 7)² + (y – 9)² = 3

(x + 7)² + (y + 9)² = 3√3

16. 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

17. 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 hyperbola

A circle

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

Ellipse

Parabola

None of these

Hyperbola

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

(0, ± a)

(-a, a)

(a, -a)

(± a, 0)

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

√3

3√3

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

22. 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

Axis of the cone

Vertex of cone

Nappe of the cone

23. 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)

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

x = r cos θ, y = r sec θ

x = r cos θ, y = sin θ

x = r cosh θ, y sin θ

x = r sec θ, y = r tan θ

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

√g²+f²–c

g+f–c

√g²–f²–c

√g²+f²+c

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

x² + y² = √5

x² + y² = 5

x² + y² = 25

(x – 3)² + y² = 5

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

Same diameter

Different centers

Same center

Same radius

28. Equation of the parabola

x² = 4ay

x = 4ay

y = 4ax

y² = 4ax²

29. Focal axis are also known as

None of these

Transverse axis

Conjugate axis

Both a and b

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

√61

31. 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 = 4

xco s θ + y sin θ = 2

xco s θ + y sin θ = √2

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

(g, f)

(f, g)

(– g, – f)

(– f, – g)

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

1/9

9/2

2/9

34. The parabola x² = y passes through

[½, ¼]

[½, ½]

[¼, ½]

(2, 2)

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

x sin θ – y cos θ = 0

x cos θ + y sin θ = 0

x sin θ + y cos θ = 0

x cos θ – y sin θ = 0

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

None of these

Inside the circle

On the circle

Outside the circle

37. Parametric equation of hyperbola are

x = asec Ø, y = b tan Ø

x = at², y = 2at

None of these

x = acos Ø, y = b = sin Ø

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

x₁ + y₁ < a²

x²₁ + y²₁ = a²

x²₁ + y²₁ < a²

x²₁ + y²₁ > a²

39. 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

40. 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

41. The parabola y² = 2x passes through

[¼, ½]

[¼, ¼]

(2, 2)

[½, ¼]

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

y – y₁ = y₁/2a (x + x₁)

yy₁ =2a (x + x₁)

xx₁ = 2a (x + y₁)

y – y₁ = 2a/x₁ (x + x₁)

43.

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

x = asec Ø, y = btan Ø

x = acos Ø, y = bsin Ø

x = atan Ø, y = bsec Ø

x = asin Ø, y = bcos Ø

45. 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 + 2gx₁ + 2fy₁ + c < 0

x₁² + y₁² = 0

46. The center of the circle is

(0, 0)

(b, a)

(a, b)

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

Normal

Slope of tangent

None of these

Tangent

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

x + y = r

x + y² = r²

x – y² = r²

x – y = r

49. 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

(x²+y²+x+y) = 0

(x₁–x₂/2 , y₁+y₂/2) = 0

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

(1, –3)

(–1, 3)

(– 1, –3)

(1, 3)

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Danial MalikLast Updated: April 18, 2025

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ECAT Mathematics Conic Section Online Test

ECAT Math Conic Section

ECAT Math Conic Section Chapter Online Test

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ECAT Math Conic Section

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