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

Radius of the circle

Center of ellipse

Center of hyperbola

Center of the circle

2. Parametric equation of hyperbola are

x = at², y = 2at

None of these

x = acos Ø, y = b = sin Ø

x = asec Ø, y = b tan Ø

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

(a, -a)

(± a, 0)

(-a, a)

(0, ± a)

4. 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

5. The parabola y² = 2x passes through

[½, ¼]

[¼, ¼]

(2, 2)

[¼, ½]

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

1/3

2/3

8/3

4/3

7. 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

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

√3

3√3

9. 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

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

(1, 1)

(-5, -3)

(-1, -1)

(0, 0)

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

(– 2/5, 2/3)

(2/3, –2/5)

(– 2/3, 2/5)

(2/5, 2/3)

12. 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

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

Two lines

A plane

A line

A sphere

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

None of these

Tangent

Normal

Slope of tangent

15. 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

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

x = acos Ø, y = bsin Ø

x = atan Ø, y = bsec Ø

x = asin Ø, y = bcos Ø

x = asec Ø, y = btan Ø

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

Axis of parabola

Directrix

Chord

Focus

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

Hyperbola

None of these

Ellipse

Parabola

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

(x – h)² + (y + k)² = r²

(x – h) + (y – k) = r²

(x – h)² + (y – k)² = r²

(x + h)² + (y + k)² = r²

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

(g, f)

(– g, – f)

(f, g)

(– f, – g)

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

√61

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

√g²+f²–c

g+f–c

√g²+f²+c

√g²–f²–c

23.

24. Focal axis are also known as

None of these

Conjugate axis

Transverse axis

Both a and b

25. 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

Page 2 of 2

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

c/a

None of these

a/c

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

Inside the circle

None of these

On the circle

Outside the circle

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

Same center

Different centers

Same radius

Same diameter

29. 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

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

9/2

1/9

2/9

31. 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

x₁ + y₁ < a²

x²₁ + y²₁ = a²

32. 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 = 0

xco s θ + y sin θ = 2

xco s θ + y sin θ = 4

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

A hyperbola

An ellipse

A circle

A parabola

34. Equation of the parabola

y² = 4ax²

x² = 4ay

x = 4ay

y = 4ax

35. The parabola x² = y passes through

(2, 2)

[½, ½]

[½, ¼]

[¼, ½]

36. 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

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

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

x + y² = r²

x – y² = r²

x + y = r

x – y = r

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 – y = 0

x² + y² + x = 0

x² + y² + y = 0

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

A ≠ B

A = 0 or B = 0

None of these

A = B ≠ 0

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

x = r cosh θ, y sin θ

x = r sec θ, y = r tan θ

x = r cos θ, y = r sec θ

x = r cos θ, y = sin θ

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

Out side the circle

One the circle

None of these

Inside the circle

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

Conics

Conic sections

None of these

Both a and b

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

(1, 3)

(1, –3)

(–1, 3)

(– 1, –3)

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

None of these

Axis of the cone

Vertices

Rulings

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

a²b²+m²

a²m²+b²

None of these

a²+b²m²

47. The center of the circle is

(a, b)

(b, a)

(0, 0)

48. Circle is special case of

Parabola

Hyperbola

None of these

Ellipse

49. 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

50. 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)

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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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