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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Page 1 of 2

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

(0, 0)

(-5, -3)

(1, 1)

(-1, -1)

2. 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

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

y – y₁ = 2a/x₁ (x + x₁)

y – y₁ = y₁/2a (x + x₁)

yy₁ =2a (x + x₁)

xx₁ = 2a (x + y₁)

4. 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 + y = 0

x² + y² – x = 0

x² + y² – y = 0

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

x = asin Ø, y = bcos Ø

x = acos Ø, y = bsin Ø

x = asec Ø, y = btan Ø

x = atan Ø, y = bsec Ø

6. 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

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

x + y² = r²

x – y² = r²

x – y = r

x + y = r

8. The center of the circle is

(0, 0)

(b, a)

(a, b)

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

(– f, – g)

(g, f)

(f, g)

(– g, – f)

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

Center of ellipse

Radius of the circle

Center of hyperbola

Center of the circle

11. The parabola y² = 2x passes through

(2, 2)

[¼, ½]

[½, ¼]

[¼, ¼]

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

Conic sections

Conics

Both a and b

None of these

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

Vertices

Axis of the cone

None of these

Rulings

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

√3

3√3

15. 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

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

A circle

A parabola

A hyperbola

An ellipse

17.

18. 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 cos θ, y = r sec θ

x = r cosh θ, y sin θ

19. 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

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

Chord

Directrix

Axis of parabola

Focus

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

√g²–f²–c

g+f–c

√g²+f²+c

√g²+f²–c

22. Equation of the parabola

y² = 4ax²

x² = 4ay

x = 4ay

y = 4ax

23. 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

24. 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

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

(–1, 3)

(1, –3)

(1, 3)

(– 1, –3)

Page 2 of 2

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

Two lines

A line

A plane

A sphere

27. 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

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

Tangent

Normal

None of these

Slope of tangent

29. Focal axis are also known as

None of these

Conjugate axis

Both a and b

Transverse axis

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

x₁ + y₁ < a²

x²₁ + y²₁ < a²

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

32. 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√3

(x + 7)² + (y + 9)² = √3

33. 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

34. Circle is special case of

None of these

Hyperbola

Parabola

Ellipse

35. Parametric equation of hyperbola are

x = at², y = 2at

x = acos Ø, y = b = sin Ø

x = asec Ø, y = b tan Ø

None of these

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

9/2

1/9

2/9

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

On the circle

Outside the circle

None of these

Inside the circle

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

c/a

None of these

a/c

39. 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 parabola

A hyperbola

40. 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

Nappe of the cone

Space of the cone

Vertex of cone

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

(± a, 0)

(a, -a)

(0, ± a)

(-a, a)

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

None of these

Ellipse

Hyperbola

Parabola

43. 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)

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

Same diameter

Same radius

Same center

Different centers

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

√61

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

xco s θ + y sin θ = 4

xco s θ – y sin θ = 0

xco s θ + y sin θ = 2

xco s θ + y sin θ = √2

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

None of these

Out side the circle

One the circle

Inside the circle

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

2/3

8/3

1/3

4/3

49. The parabola x² = y passes through

[½, ½]

[½, ¼]

[¼, ½]

(2, 2)

50. 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

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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

ECAT Math Conic Section Chapter Online Test

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