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

x + y = r

x – y = r

x – y² = r²

x + y² = r²

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

x² + y² = 5

x² + y² = 25

(x – 3)² + y² = 5

x² + y² = √5

3. The center of the circle is

(a, b)

(0, 0)

(b, a)

4. 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 > a²

x²₁ + y²₁ +2gx₁ + 2fy₁ + c

√x²₁ + y²₁ +2gx₁ + 2fy₁ + c

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

Chord

Axis of parabola

Directrix

Focus

6. The parabola y² = 2x passes through

[½, ¼]

[¼, ¼]

[¼, ½]

(2, 2)

7. 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

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

One the circle

Out side the circle

None of these

Inside the circle

9. Circle is special case of

Ellipse

None of these

Hyperbola

Parabola

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

(–1, 3)

(– 1, –3)

(1, 3)

(1, –3)

11. 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 + y = 0

x² + y² + x = 0

x² + y² – x = 0

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

√g²–f²–c

√g²+f²–c

√g²+f²+c

g+f–c

13. 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 parabola

A circle

An ellipse

14. Equation of the parabola

y = 4ax

x² = 4ay

x = 4ay

y² = 4ax²

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

Same radius

Same center

Same diameter

Different centers

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

(0, 0)

(1, 1)

(-1, -1)

(-5, -3)

17. 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

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

1/9

9/2

2/9

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

(– 2/5, 2/3)

(– 2/3, 2/5)

(2/5, 2/3)

(2/3, –2/5)

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

None of these

Vertices

Rulings

Axis of the cone

21. 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 = 2

xco s θ – y sin θ = 0

xco s θ + y sin θ = 4

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

√61

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

a²b²+m²

a²+b²m²

None of these

a²m²+b²

24. Parametric equation of hyperbola are

x = at², y = 2at

x = asec Ø, y = b tan Ø

x = acos Ø, y = b = sin Ø

None of these

25. 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

Page 2 of 2

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

27. Focal axis are also known as

Both a and b

Conjugate axis

None of these

Transverse axis

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

Inside the circle

Outside the circle

On the circle

None of these

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

Center of hyperbola

Radius of the circle

Center of the circle

Center of ellipse

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

√3

3√3

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

x = asin Ø, y = bcos Ø

x = atan Ø, y = bsec Ø

x = asec Ø, y = btan Ø

x = acos Ø, y = bsin Ø

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

Ellipse

Parabola

None of these

Hyperbola

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

(0, ± a)

(a, -a)

(± a, 0)

(-a, a)

34. The parabola x² = y passes through

[¼, ½]

(2, 2)

[½, ½]

[½, ¼]

35. 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

Nappe of the cone

Axis of the cone

Vertex of cone

Space of the cone

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

yy₁ =2a (x + x₁)

xx₁ = 2a (x + y₁)

y – y₁ = y₁/2a (x + x₁)

y – y₁ = 2a/x₁ (x + x₁)

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

A circle

A hyperbola

An ellipse

A parabola

38. 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

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

a/c

None of these

c/a

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

A ≠ B

A = B ≠ 0

None of these

A = 0 or B = 0

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

8/3

4/3

1/3

2/3

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

A line

A plane

A sphere

Two lines

43. 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 cos θ, y = sin θ

x = r cosh θ, y sin θ

44. 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

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

Conic sections

Both a and b

None of these

Conics

46. 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

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

(g, f)

(f, g)

(– g, – f)

(– f, – g)

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

Normal

Slope of tangent

Tangent

None of these

49. 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

50.

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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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