Mathematics Conic Section Online Test

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Question 1

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

Answer

x – y = r

Answer

x + y² = r²

Answer

x – y² = r²

Question 2

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

Answer

A = 0 or B = 0

Answer

None of these

Answer

A = B ≠ 0

Question 3

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

Answer

x = r sec θ, y = r tan θ

Answer

x = r cos θ, y = r sec θ

Answer

x = r cos θ, y = sin θ

Answer

x = r cosh θ, y sin θ

Question 4

4. Equation of the parabola

Answer

y² = 4ax²

Question 5

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

Question 6

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

Answer

A parabola

Answer

A hyperbola

Answer

An ellipse

Question 7

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

Answer

x² + y² = 25

Answer

x² + y² = 5

Answer

(x – 3)² + y² = 5

Answer

x² + y² = √5

Question 8

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

Answer

Axis of parabola

Question 9

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

Question 10

10. 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 11

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

Answer

(– f, – g)

Answer

(– g, – f)

Question 12

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

Question 13

13. 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 14

14. 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 15

15. The parabola y² = 2x passes through

Question 16

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

Answer

None of these

Answer

Inside the circle

Answer

Out side the circle

Answer

One the circle

Question 17

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

Answer

x₁² + y₁² + 2gx₁ + 2fy₁ + c > 0

Answer

x₁² + y₁² + 2gx₁ + 2fy₁ + c = 0

Answer

x₁² + y₁² + 2gx₁ + 2fy₁ + c < 0

Answer

x₁² + y₁² = 0

Question 18

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

Question 19

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

Answer

Slope of tangent

Answer

None of these

Question 20

20. 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 + y = 0

Answer

x² + y² + x = 0

Question 21

21. Circle is special case of

Answer

None of these

Question 22

22. 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 +2gx₁ + 2fy₁ + c

Answer

x²₁ + y²₁ > a²

Answer

√x²₁ + y²₁ +2gx₁ + 2fy₁ + c

Answer

√x²₁ + y²₁ = a²

Question 23

23. The center of the circle is

Question 24

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

Answer

(– 2/5, 2/3)

Answer

(2/5, 2/3)

Answer

(– 2/3, 2/5)

Answer

(2/3, –2/5)

Question 25

25. 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 26

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

Answer

Different centers

Answer

Same diameter

Answer

Same center

Answer

Same radius

Question 27

27. The parabola x² = y passes through

Question 28

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

Question 29

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

Answer

Center of the circle

Answer

Center of hyperbola

Answer

Radius of the circle

Answer

Center of ellipse

Question 30

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

Answer

None of these

Answer

Axis of the cone

Question 31

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

Answer

x₁ + y₁ < a²

Answer

x²₁ + y²₁ < a²

Answer

x²₁ + y²₁ = a²

Answer

x²₁ + y²₁ > a²

Question 32

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

Question 33

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

Answer

On the circle

Answer

None of these

Answer

Outside the circle

Answer

Inside the circle

Question 34

34. 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

(x²+y²+x+y) = 0

Answer

(x₁+x₂/2 , y₁+y₂/2) = 0

Answer

(x₁–x₂/2 , y₁+y₂/2) = 0

Question 35

35. Focal axis are also known as

Answer

Transverse axis

Answer

None of these

Answer

Both a and b

Answer

Conjugate axis

Question 36

36. 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

Answer

Nappe of the cone

Answer

Axis of the cone

Answer

Vertex of cone

Question 37

37. Parametric equation of hyperbola are

Answer

None of these

Answer

x = asec Ø, y = b tan Ø

Answer

x = at², y = 2at

Answer

x = acos Ø, y = b = sin Ø

Question 38

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

Answer

None of these

Question 39

39.

Question 40

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

Answer

x = asin Ø, y = bcos Ø

Answer

x = atan Ø, y = bsec Ø

Answer

x = acos Ø, y = bsin Ø

Answer

x = asec Ø, y = btan Ø

Question 41

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

Answer

y – y₁ = y₁/2a (x + x₁)

Answer

yy₁ =2a (x + x₁)

Answer

xx₁ = 2a (x + y₁)

Answer

y – y₁ = 2a/x₁ (x + x₁)

Question 42

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

Answer

(x + 7)² + (y + 9)² = 9

Answer

(x – 7)² + (y – 9)² = 3

Answer

(x + 7)² + (y + 9)² = √3

Answer

(x + 7)² + (y + 9)² = 3√3

Question 43

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

Answer

a²+b²m²

Answer

a²m²+b²

Answer

a²b²+m²

Answer

None of these

Question 44

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

Answer

None of these

Question 45

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

Question 46

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

Answer

xco s θ + y sin θ = 2

Answer

xco s θ – y sin θ = 0

Answer

xco s θ + y sin θ = √2

Answer

xco s θ + y sin θ = 4

Question 47

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

Question 48

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

Answer

(– 1, –3)

Question 49

49. 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 50

50. 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 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

Math Conic Section Practice Test Online With Explanation

How to Score High in Mathematics Conic Section Online Test?

Key Preparation Tips:

More Related Resources

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