TRB BT Assistant - General Polar Equations of Conics Online Test (MCQ Quiz)

1. In polar coordinates, what is the general form of a conic section with eccentricity 'e' and a focus at the origin?

A) r = ed / (1 + e cos θ) B) r = ed / (1 - e sin θ) C) r = ed / (e + cos θ) D) r = e / (d + cos θ)

2. What does the parameter 'd' represent in the polar equation of a conic section r = ed / (1 + e cos θ)?

A) Eccentricity B) Semi-latus rectum C) Directrix distance from the focus D) Focal length

3. If the eccentricity 'e' of a conic section in polar form is equal to 1, what type of conic is it?

A) Ellipse B) Hyperbola C) Parabola D) Circle

4. For a conic section in polar coordinates, if e > 1, what type of conic is represented by the equation r = ed / (1 + e cos θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

5. What type of conic section is represented by the polar equation r = ed / (1 + e cos θ) when 0 < e < 1?

A) Parabola B) Hyperbola C) Ellipse D) Circle

6. Consider the polar equation r = 5 / (1 + 2 cos θ). What is the eccentricity 'e' of this conic section?

A) 1/2 B) 1 C) 2 D) 5

7. In the equation r = 8 / (3 - 3 sin θ), what adjustment is needed to match the standard polar form r = ed / (1 ± e sin θ) or r = ed / (1 ± e cos θ)?

A) Divide numerator and denominator by 3 B) Multiply numerator and denominator by 3 C) Subtract 3 from the numerator D) Add 3 to the denominator

8. What type of conic is represented by r = 12 / (4 + 3 cos θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

9. If a polar equation of a conic is given by r = 6 / (1 - sin θ), what is its eccentricity?

A) 0 B) 1 C) 1/6 D) 6

10. What conic section is described by the polar equation r = 10 / (2 + 2 cos θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

11. For the polar equation r = 7 / (5 - 3 sin θ), what is the value of 'd' after normalizing the denominator to have a leading coefficient of 1?

A) 7/5 B) 5/7 C) 3/5 D) 5/3

12. What is the directrix distance 'd' for the conic r = 4 / (1 + cos θ)?

A) 1 B) 4 C) 1/4 D) 2

13. The polar equation r = 3 / (2 - sin θ) represents a conic section. What is the nature of this conic?

A) Ellipse (e = 1/2) B) Parabola (e = 1) C) Hyperbola (e = 2) D) Circle (e = 0)

14. Which of the following polar equations represents a parabola with its focus at the origin and directrix x = 4?

A) r = 4 / (1 + cos θ) B) r = 2 / (1 + cos θ) C) r = 4 / (2 + cos θ) D) r = 1 / (1 + cos θ)

15. What is the semi-latus rectum 'l' for a conic section with the polar equation r = ed / (1 + e cos θ)?

A) ed B) e/d C) d/e D) 1/ed

16. Consider the polar equation r = 5 / (1 - 2 sin θ). What is the eccentricity 'e' of this conic?

A) 1/2 B) 1 C) 2 D) 5

17. The polar equation r = 3 / (1 + sin θ) represents a parabola. What is the distance of the directrix from the focus?

A) 1 B) 3 C) 1/3 D) 0

18. What type of conic is represented by r = 10 / (3 + 4 cos θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

19. If a conic section has the polar equation r = 6 / (2 + 2 cos θ), what is its eccentricity?

A) 1/2 B) 1 C) 2 D) 3

20. In the equation r = 8 / (1 - 3 sin θ), what is the value of 'd' when expressed in the standard form r = ed / (1 ± e sin θ)?

A) 8 B) 1/3 C) 3 D) 8/3

21. Which conic section is described by the polar equation r = 2 / (1 + cos θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

22. What is the directrix for the conic section r = 5 / (1 + 0.5 cos θ)?

A) x = 10 B) x = 5 C) y = 10 D) y = 5

23. Consider the polar equation r = 15 / (3 - 3 sin θ). What is the eccentricity of this conic?

A) 1/3 B) 1 C) 3 D) 5

24. The polar equation r = 12 / (5 - 4 cos θ) represents a conic. What is the distance of the directrix from the focus?

A) 12/5 B) 5/12 C) 4/5 D) 5/4

25. What type of conic is given by the polar equation r = 9 / (1 - sin θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

26. For the polar equation r = 7 / (2 + 3 cos θ), what is the value of 'd' after normalizing the denominator?

A) 7/2 B) 2/7 C) 3/2 D) 2/3

27. If the polar equation of a conic is r = 10 / (1 + e cos θ), and it passes through the point (r, θ) = (5, 0), what is the value of 'e'?

A) 1/5 B) 2/5 C) 3/5 D) 4/5

28. What does the term 'ed' represent in the polar equation of a conic, where 'e' is eccentricity and 'd' is the distance of the directrix from the focus?

A) Semi-major axis B) Semi-latus rectum C) Focal length D) Directrix equation

29. Consider the equation r = 8 / (1 - cos θ). What is the eccentricity 'e'?

A) 0 B) 1 C) 8 D) 1/8

30. What type of conic section is represented by r = 6 / (2 + sin θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

31. The polar equation r = 4 / (1 - 2 cos θ) describes a conic. What is its eccentricity?

A) 1/2 B) 1 C) 2 D) 4

32. What is the distance of the directrix from the focus for the conic r = 3 / (1 + 0.75 cos θ)?

A) 1 B) 3/0.75 C) 0.75 D) 3

33. Which polar equation represents a hyperbola with eccentricity e = 2 and focus at the origin, with a directrix y = 3?

A) r = 6 / (1 + 2 sin θ) B) r = 3 / (1 + 2 sin θ) C) r = 6 / (2 + sin θ) D) r = 3 / (2 + sin θ)

34. If a conic has the polar equation r = ed / (1 - e sin θ), and e < 1, what type of conic is it?

A) Parabola B) Hyperbola C) Ellipse D) Circle

35. What is the value of 'd' for the polar equation r = 12 / (1 + cos θ)?

A) 1 B) 12 C) 1/12 D) 2

36. The polar equation r = 5 / (2 - 2 cos θ) represents a conic. What is its eccentricity?

A) 1/2 B) 1 C) 2 D) 5/2

37. Consider the polar equation r = 7 / (1 + 0.5 sin θ). What is the directrix distance 'd'?

A) 0.5 B) 1 C) 7 D) 14

38. What type of conic is represented by r = 10 / (5 + 5 cos θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

39. For the polar equation r = 8 / (3 + 4 sin θ), what is the eccentricity 'e'?

A) 3/4 B) 4/3 C) 3/8 D) 8/3

40. If a conic section has the polar equation r = ed / (1 + e cos θ) and e = 1, what is the shape of the conic?

A) Circle B) Ellipse C) Parabola D) Hyperbola

41. What is the semi-latus rectum for the conic r = 6 / (1 + 2 cos θ)?

A) 6 B) 3 C) 12 D) 2

42. The polar equation r = 2 / (1 - cos θ) represents a parabola. What is the distance of the directrix from the focus?

A) 1 B) 2 C) 1/2 D) 0

43. What type of conic is described by r = 15 / (3 + 5 sin θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

44. Consider the polar equation r = 10 / (1 - 0.5 sin θ). What is the value of 'd' for this conic?

A) 0.5 B) 1 C) 10 D) 20

45. If the polar equation of a conic is r = 5 / (2 + 2 cos θ), what is its eccentricity?

A) 1/2 B) 1 C) 2 D) 5/2

46. What is the directrix equation for the conic r = 9 / (1 - sin θ)?

A) y = 9 B) y = -9 C) x = 9 D) x = -9

47. The polar equation r = 12 / (4 - 3 cos θ) represents a conic. What is its eccentricity?

A) 3/4 B) 4/3 C) 3/12 D) 12/3

48. What type of conic is represented by r = 7 / (1 + sin θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

49. In the polar equation r = 20 / (5 - 4 sin θ), what is the semi-latus rectum 'l'?

A) 20/5 B) 4 C) 5 D) 20

50. What conic section is described by r = 1 / (1 + cos θ)?

A) Ellipse B) Parabola C) Hyperbola D) Circle

General Polar Equations of Conics - Online Test

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