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

Axis of the cone

None of these

Vertices

Rulings

2. Focal axis are also known as

Transverse axis

None of these

Conjugate axis

Both a and b

3. 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 = 2

xco s θ + y sin θ = 4

4. 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

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

1/3

2/3

4/3

8/3

6. 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)

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

Chord

Focus

Axis of parabola

Directrix

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

(g, f)

(– f, – g)

(f, g)

(– g, – f)

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

x sin θ – y cos θ = 0

x sin θ + y cos θ = 0

x cos θ – y sin θ = 0

x cos θ + y sin θ = 0

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 – y = 0

x² + y² – x = 0

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

Normal

Slope of tangent

None of these

Tangent

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

A circle

An ellipse

A hyperbola

A parabola

13. The center of the circle is

(0, 0)

(b, a)

(a, b)

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

3√3

√3

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

A hyperbola

A parabola

A circle

An ellipse

16. The parabola x² = y passes through

[½, ¼]

(2, 2)

[½, ½]

[¼, ½]

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

Both a and b

Conic sections

Conics

None of these

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

a²+b²m²

a²m²+b²

None of these

a²b²+m²

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

(x + 7)² + (y + 9)² = 3√3

(x + 7)² + (y + 9)² = 9

(x – 7)² + (y – 9)² = 3

(x + 7)² + (y + 9)² = √3

20. 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

Vertex of cone

Nappe of the cone

Axis of the cone

Space of the cone

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

x = r sec θ, y = r tan θ

x = r cos θ, y = sin θ

x = r cosh θ, y sin θ

x = r cos θ, y = r sec θ

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

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

Parabola

Ellipse

Hyperbola

None of these

24. Equation of the parabola

x² = 4ay

x = 4ay

y² = 4ax²

y = 4ax

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

(-5, -3)

(-1, -1)

(0, 0)

(1, 1)

Page 2 of 2

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

Center of the circle

Center of hyperbola

Radius of the circle

Center of ellipse

27. The parabola y² = 2x passes through

[¼, ½]

[½, ¼]

[¼, ¼]

(2, 2)

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

x² + y² = 25

(x – 3)² + y² = 5

x² + y² = 5

x² + y² = √5

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

√61

30. 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

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

A plane

A sphere

A line

Two lines

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

x + y = r

x + y² = r²

x – y = r

x – y² = r²

33. 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

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

Same diameter

Same center

Different centers

Same radius

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

9/2

2/9

1/9

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

(1, 3)

(– 1, –3)

(–1, 3)

(1, –3)

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

None of these

A ≠ B

A = B ≠ 0

A = 0 or B = 0

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

√g²+f²+c

√g²+f²–c

√g²–f²–c

g+f–c

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

yy₁ =2a (x + x₁)

xx₁ = 2a (x + y₁)

y – y₁ = 2a/x₁ (x + x₁)

y – y₁ = y₁/2a (x + x₁)

40.

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

None of these

c/a

a/c

42. 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

43. Parametric equation of hyperbola are

None of these

x = asec Ø, y = b tan Ø

x = acos Ø, y = b = sin Ø

x = at², y = 2at

44. 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

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

Inside the circle

None of these

Outside the circle

On the circle

46. 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

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

(-a, a)

(0, ± a)

(± a, 0)

(a, -a)

48. 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

49. 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

50. Circle is special case of

Hyperbola

Parabola

Ellipse

None of these

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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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