ECAT Mathematics Conic Section Online Test

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

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

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

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

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

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

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

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

9. The parabola y² = 2x passes through

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

11. Equation of the parabola

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

13. The parabola x² = y passes through

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

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

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

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

18. Circle is special case of

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

20. Parametric equation of hyperbola are

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

23. Focal axis are also known as

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

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

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

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

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

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

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

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

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

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

34. 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

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

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

37. The center of the circle is

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

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

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

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

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

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

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

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

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

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

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

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

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