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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Page 1 of 2

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

Out side the circle

Inside the circle

One the circle

None of these

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

Rulings

Vertices

Axis of the cone

None of these

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

An ellipse

A parabola

A hyperbola

A circle

4. Equation of the parabola

y = 4ax

x = 4ay

x² = 4ay

y² = 4ax²

6. Focal axis are also known as

Conjugate axis

Both a and b

Transverse axis

None of these

7. 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

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

Conic sections

None of these

Conics

Both a and b

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

(– f, – g)

(f, g)

(– g, – f)

(g, f)

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

Slope of tangent

None of these

Normal

Tangent

11. 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

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. Parametric equation of hyperbola are

x = asec Ø, y = b tan Ø

x = acos Ø, y = b = sin Ø

None of these

x = at², y = 2at

14. Circle is special case of

None of these

Hyperbola

Parabola

Ellipse

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

A line

A plane

A sphere

Two lines

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

g+f–c

√g²+f²+c

√g²+f²–c

√g²–f²–c

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

c/a

a/c

None of these

18. The parabola y² = 2x passes through

(2, 2)

[¼, ½]

[¼, ¼]

[½, ¼]

19. 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

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

None of these

a²m²+b²

a²b²+m²

a²+b²m²

21. 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

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

On the circle

Inside the circle

Outside the circle

None of these

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

y – y₁ = y₁/2a (x + x₁)

y – y₁ = 2a/x₁ (x + x₁)

yy₁ =2a (x + x₁)

xx₁ = 2a (x + y₁)

24. 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)

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

Center of the circle

Radius of the circle

Center of ellipse

Center of hyperbola

Page 2 of 2

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

9/2

2/9

1/9

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

3√3

√3

28. The parabola x² = y passes through

[¼, ½]

[½, ¼]

(2, 2)

[½, ½]

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

Same radius

Same center

Same diameter

Different centers

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

x – y² = r²

x + y² = r²

x + y = r

x – y = r

31. 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

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

A = 0 or B = 0

A ≠ B

None of these

A = B ≠ 0

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

34. 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

35. 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 – x = 0

x² + y² – y = 0

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

x = r cos θ, y = sin θ

x = r sec θ, y = r tan θ

x = r cosh θ, y sin θ

x = r cos θ, y = r sec θ

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

(– 1, –3)

(1, 3)

(1, –3)

(–1, 3)

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

None of these

Parabola

Hyperbola

Ellipse

39. 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

40. Point (x₁, y₁) lies inside the circle x²+y²+2gx+2fy+c= 0 if

x₁² + y₁² + 2gx₁ + 2fy₁ + c = 0

x₁² + y₁² = 0

x₁² + y₁² + 2gx₁ + 2fy₁ + c < 0

x₁² + y₁² + 2gx₁ + 2fy₁ + c > 0

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

(0, 0)

(-5, -3)

(1, 1)

(-1, -1)

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

(-a, a)

(± a, 0)

(0, ± a)

(a, -a)

43. 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

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

Axis of parabola

Chord

Directrix

Focus

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

2/3

4/3

1/3

8/3

46. 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 sin θ + y cos θ = 0

x cos θ – y sin θ = 0

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

x = asec Ø, y = btan Ø

x = asin Ø, y = bcos Ø

x = acos Ø, y = bsin Ø

x = atan Ø, y = bsec Ø

48. The center of the circle is

(0, 0)

(b, a)

(a, b)

49. 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

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

√61

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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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