Mathematics Conic Section Online Test

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Question 1

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

Answer

x² + y² – x = 0

Answer

x² + y² + x = 0

Answer

x² + y² – y = 0

Answer

x² + y² + y = 0

Question 2

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

Answer

x = r cosh θ, y sin θ

Answer

x = r cos θ, y = r sec θ

Answer

x = r cos θ, y = sin θ

Answer

x = r sec θ, y = r tan θ

Question 3

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

Question 4

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

Question 5

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

Question 6

6. Parametric equation of hyperbola are

Answer

x = acos Ø, y = b = sin Ø

Answer

None of these

Answer

x = at², y = 2at

Answer

x = asec Ø, y = b tan Ø

Question 7

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

Answer

(– f, – g)

Answer

(– g, – f)

Question 8

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

Answer

x²₁ + y²₁ > a²

Answer

x²₁ + y²₁ +2gx₁ + 2fy₁ + c

Answer

√x²₁ + y²₁ = a²

Answer

√x²₁ + y²₁ +2gx₁ + 2fy₁ + c

Question 9

9. Focal axis are also known as

Answer

Both a and b

Answer

Transverse axis

Answer

None of these

Answer

Conjugate axis

Question 10

10. Equation of the parabola

Answer

y² = 4ax²

Question 11

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

Answer

Different centers

Answer

Same center

Answer

Same radius

Answer

Same diameter

Question 12

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

Answer

x²₁ + y²₁ = a²

Answer

x²₁ + y²₁ < a²

Answer

x²₁ + y²₁ > a²

Answer

x₁ + y₁ < a²

Question 13

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

Answer

xco s θ – y sin θ = 0

Answer

xco s θ + y sin θ = 2

Answer

xco s θ + y sin θ = 4

Answer

xco s θ + y sin θ = √2

Question 14

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

Answer

xx₁ = 2a (x + y₁)

Answer

y – y₁ = y₁/2a (x + x₁)

Answer

y – y₁ = 2a/x₁ (x + x₁)

Answer

yy₁ =2a (x + x₁)

Question 15

15.

Question 16

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

Answer

None of these

Answer

a²m²+b²

Answer

a²b²+m²

Answer

a²+b²m²

Question 17

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

Question 18

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

Answer

x = asec Ø, y = btan Ø

Answer

x = acos Ø, y = bsin Ø

Answer

x = atan Ø, y = bsec Ø

Answer

x = asin Ø, y = bcos Ø

Question 19

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

Answer

A parabola

Answer

An ellipse

Answer

A hyperbola

Question 20

20. The parabola x² = y passes through

Question 21

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

Answer

Axis of the cone

Answer

None of these

Question 22

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

Answer

x² + y² – y = 0

Answer

x² + y² + y = 0

Answer

x² + y² + x = 0

Answer

x² + y² – x = 0

Question 23

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

Question 24

24. The center of the circle is

Question 25

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

Answer

None of these

Question 26

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

Answer

(x + h)² + (y + k)² = r²

Answer

(x – h) + (y – k) = r²

Answer

(x – h)² + (y + k)² = r²

Answer

(x – h)² + (y – k)² = r²

Question 27

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

Answer

(x²+y²+x+y) = 0

Answer

(x₁–x₂/2 , y₁–y₂/2) = 0

Answer

(x₁–x₂/2 , y₁+y₂/2) = 0

Answer

(x₁+x₂/2 , y₁+y₂/2) = 0

Question 28

28. 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 29

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

Answer

(– 2/3, 2/5)

Answer

(– 2/5, 2/3)

Answer

(2/3, –2/5)

Answer

(2/5, 2/3)

Question 30

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

Answer

(– 1, –3)

Question 31

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

Answer

Both a and b

Answer

Conic sections

Answer

None of these

Question 32

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

Answer

None of these

Question 33

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

Question 34

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

Answer

x sin θ – y cos θ = 0

Answer

x sin θ + y cos θ = 0

Answer

x cos θ – y sin θ = 0

Answer

x cos θ + y sin θ = 0

Question 35

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

Question 36

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

Answer

x₁² + y₁² + 2gx₁ + 2fy₁ + c < 0

Answer

x₁² + y₁² = 0

Answer

x₁² + y₁² + 2gx₁ + 2fy₁ + c = 0

Answer

x₁² + y₁² + 2gx₁ + 2fy₁ + c > 0

Question 37

37. Circle is special case of

Answer

None of these

Question 38

38. 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 39

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

Answer

Center of ellipse

Answer

Center of the circle

Answer

Radius of the circle

Answer

Center of hyperbola

Question 40

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

Answer

(x – 3)² + y² = 5

Answer

x² + y² = 5

Answer

x² + y² = √5

Answer

x² + y² = 25

Question 41

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

Answer

None of these

Answer

On the circle

Answer

Outside the circle

Answer

Inside the circle

Question 42

42. 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

Nappe of the cone

Answer

Axis of the cone

Answer

Vertex of cone

Answer

Space of the cone

Question 43

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

Answer

A = 0 or B = 0

Answer

A = B ≠ 0

Answer

None of these

Question 44

44. The parabola y² = 2x passes through

Question 45

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

Answer

x – y² = r²

Answer

x – y = r

Answer

x + y² = r²

Question 46

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

Answer

Slope of tangent

Answer

None of these

Question 47

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

Answer

Axis of parabola

Question 48

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

Question 49

49. 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 parabola

Answer

A hyperbola

Answer

An ellipse

Question 50

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

Answer

Inside the circle

Answer

One the circle

Answer

None of these

Answer

Out side the circle

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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Key Preparation Tips:

More Related Resources

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