Mathematics Conic Section Online Test

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Question 1

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

Answer

Axis of the cone

Answer

None of these

Question 2

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

Answer

A = B ≠ 0

Answer

None of these

Answer

A = 0 or B = 0

Question 3

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

Answer

Center of ellipse

Answer

Center of the circle

Answer

Center of hyperbola

Answer

Radius of the circle

Question 4

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

Question 5

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

Answer

A hyperbola

Answer

A parabola

Answer

An ellipse

Question 6

6. The square of the length of the tangent from the point P(x₁y₁) to the circle x² + y² + 2gx + 2fy + c = 0 is

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√x²₁ + y²₁ = a²

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x²₁ + y²₁ +2gx₁ + 2fy₁ + c

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x²₁ + y²₁ > a²

Answer

√x²₁ + y²₁ +2gx₁ + 2fy₁ + c

Question 7

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

Question 8

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

Answer

(x – 3)² + y² = 5

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x² + y² = 5

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x² + y² = 25

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x² + y² = √5

Question 9

9. Circle is special case of

Answer

None of these

Question 10

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

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None of these

Question 11

11. Focal axis are also known as

Answer

Both a and b

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Conjugate axis

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Transverse axis

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None of these

Question 12

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

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x = r cosh θ, y sin θ

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x = r cos θ, y = r sec θ

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x = r sec θ, y = r tan θ

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x = r cos θ, y = sin θ

Question 13

13. Parametric equation of hyperbola are

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x = at², y = 2at

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x = asec Ø, y = b tan Ø

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x = acos Ø, y = b = sin Ø

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None of these

Question 14

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

Question 15

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

Answer

None of these

Answer

Slope of tangent

Question 16

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

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(– 1, –3)

Question 17

17. The parabola x² = y passes through

Question 18

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

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Inside the circle

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Out side the circle

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One the circle

Answer

None of these

Question 19

19. If A (0, 0) and (– 1, 0) are ends of the diameter, then the equation fo the circle is

Answer

x² + y² + y = 0

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x² + y² + x = 0

Answer

x² + y² – x = 0

Answer

x² + y² – y = 0

Question 20

20.

Question 21

21. The tangents drawn from the point (x₁, y₁) to the circle x² + y² = a² are real and distinct if

Answer

x²₁ + y²₁ < a²

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x₁ + y₁ < a²

Answer

x²₁ + y²₁ = a²

Answer

x²₁ + y²₁ > a²

Question 22

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

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x cos θ + y sin θ = 0

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x sin θ – y cos θ = 0

Answer

x cos θ – y sin θ = 0

Answer

x sin θ + y cos θ = 0

Question 23

23. The parabola y² = 2x passes through

Question 24

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

Question 25

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

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x₁² + y₁² = 0

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x₁² + y₁² + 2gx₁ + 2fy₁ + c > 0

Answer

x₁² + y₁² + 2gx₁ + 2fy₁ + c < 0

Answer

x₁² + y₁² + 2gx₁ + 2fy₁ + c = 0

Question 26

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

Answer

(2/3, –2/5)

Answer

(– 2/3, 2/5)

Answer

(2/5, 2/3)

Answer

(– 2/5, 2/3)

Question 27

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

Question 28

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

Answer

Axis of parabola

Question 29

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

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x – y² = r²

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x + y² = r²

Answer

x – y = r

Question 30

30. The center of the circle is

Question 31

31. Equation of the parabola

Answer

y² = 4ax²

Question 32

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

Answer

A hyperbola

Answer

A parabola

Answer

An ellipse

Question 33

33. 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

Answer

Space of the cone

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Nappe of the cone

Answer

Axis of the cone

Answer

Vertex of cone

Question 34

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

Question 35

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

Answer

None of these

Answer

Outside the circle

Answer

On the circle

Answer

Inside the circle

Question 36

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

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x = asec Ø, y = btan Ø

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x = asin Ø, y = bcos Ø

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x = acos Ø, y = bsin Ø

Answer

x = atan Ø, y = bsec Ø

Question 37

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

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(x – h) + (y – k) = r²

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(x – h)² + (y – k)² = r²

Answer

(x – h)² + (y + k)² = r²

Answer

(x + h)² + (y + k)² = r²

Question 38

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

Answer

Same diameter

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Different centers

Answer

Same radius

Answer

Same center

Question 39

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

Answer

y – y₁ = y₁/2a (x + x₁)

Answer

xx₁ = 2a (x + y₁)

Answer

yy₁ =2a (x + x₁)

Answer

y – y₁ = 2a/x₁ (x + x₁)

Question 40

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

Answer

xco s θ + y sin θ = √2

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xco s θ – y sin θ = 0

Answer

xco s θ + y sin θ = 2

Answer

xco s θ + y sin θ = 4

Question 41

41. If A (0, 0) and (0, 1) are ends of the diameter, then the equation of the circle is

Answer

x² + y² – x = 0

Answer

x² + y² + y = 0

Answer

x² + y² + x = 0

Answer

x² + y² – y = 0

Question 42

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

Answer

(x + 7)² + (y + 9)² = 3√3

Answer

(x + 7)² + (y + 9)² = 9

Answer

(x – 7)² + (y – 9)² = 3

Answer

(x + 7)² + (y + 9)² = √3

Question 43

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

Answer

None of these

Question 44

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

Question 45

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

Question 46

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

Answer

None of these

Answer

Both a and b

Answer

Conic sections

Question 47

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

Answer

√g²–f²–c

Answer

√g²+f²–c

Answer

√g²+f²+c

Question 48

48. If A (x₁, y₁) and (x₂ – y₂) are ends of the diameter, then the center of the circle is

Answer

(x₁–x₂/2 , y₁–y₂/2) = 0

Answer

(x₁+x₂/2 , y₁+y₂/2) = 0

Answer

(x₁–x₂/2 , y₁+y₂/2) = 0

Answer

(x²+y²+x+y) = 0

Question 49

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

Answer

(– g, – f)

Answer

(– f, – g)

Question 50

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

Answer

a²m²+b²

Answer

a²+b²m²

Answer

None of these

Answer

a²b²+m²

Question 51

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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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Important Math Conic Section Question and Answer

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Maan Ali

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