JEE (Main) Mathematics - Circle and Conic Sections MCQs

31. The equation of a circle with center (2, -3) and radius 5 is:
    • A) \( (x - 2)^2 + (y + 3)^2 = 25 \)
    • B) \( (x + 2)^2 + (y - 3)^2 = 25 \)
    • C) \( (x - 2)^2 + (y - 3)^2 = 25 \) (Answer)
    • D) \( (x + 2)^2 + (y + 3)^2 = 25 \)
32. The center and radius of the circle \( x^2 + y^2 - 6x + 8y - 11 = 0 \) are:
    • A) (3, -4), 6
    • B) (-3, 4), 6
    • C) (3, -4), 5 (Answer)
    • D) (3, -4), 7
33. If the endpoints of a diameter of a circle are (1, 2) and (7, 6), the equation of the circle is:
    • A) \( (x - 4)^2 + (y - 4)^2 = 25 \) (Answer)
    • B) \( (x + 4)^2 + (y + 4)^2 = 25 \)
    • C) \( (x - 4)^2 + (y - 4)^2 = 20 \)
    • D) \( (x + 4)^2 + (y + 4)^2 = 20 \)
34. The equation of a circle passing through the origin and having center at (2, 3) is:
    • A) \( (x - 2)^2 + (y - 3)^2 = 13 \) (Answer)
    • B) \( (x + 2)^2 + (y + 3)^2 = 13 \)
    • C) \( (x - 2)^2 + (y - 3)^2 = 9 \)
    • D) \( (x + 2)^2 + (y + 3)^2 = 9 \)
35. The length of the chord of the circle \( x^2 + y^2 = 25 \) intercepted by the line \( x + y = 5 \) is:
    • A) \( 5 \sqrt{2} \) (Answer)
    • B) \( 5 \sqrt{3} \)
    • C) 10
    • D) 5
36. The equation of a parabola with vertex at the origin and focus at (0, 2) is:
    • A) \( x^2 = 8y \) (Answer)
    • B) \( y^2 = 8x \)
    • C) \( x^2 + y^2 = 8 \)
    • D) \( x^2 - y^2 = 8 \)
37. The latus rectum of the parabola \( y^2 = 12x \) is:
    • A) 6
    • B) 12 (Answer)
    • C) 24
    • D) 3
38. The focus of the parabola \( x^2 = -4y \) is:
    • A) (0, -1)
    • B) (0, -2) (Answer)
    • C) (1, 0)
    • D) (2, 0)
39. The equation of an ellipse with vertices at \( (±6, 0) \) and foci at \( (±4, 0) \) is:
    • A) \( \frac{x^2}{36} + \frac{y^2}{20} = 1 \) (Answer)
    • B) \( \frac{x^2}{20} + \frac{y^2}{36} = 1 \)
    • C) \( \frac{x^2}{20} - \frac{y^2}{36} = 1 \)
    • D) \( \frac{x^2}{36} - \frac{y^2}{20} = 1 \)
40. The eccentricity of the ellipse \( \frac{x^2}{25} + \frac{y^2}{16} = 1 \) is:
    • A) \( \frac{3}{5} \) (Answer)
    • B) \( \frac{4}{5} \)
    • C) \( \frac{5}{3} \)
    • D) \( \frac{5}{4} \)
41. The equation of a hyperbola with foci at \( (±5, 0) \) and vertices at \( (±3, 0) \) is:
    • A) \( \frac{x^2}{9} - \frac{y^2}{16} = 1 \) (Answer)
    • B) \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \)
    • C) \( \frac{y^2}{9} - \frac{x^2}{16} = 1 \)
    • D) \( \frac{y^2}{16} - \frac{x^2}{9} = 1 \)
42. The asymptotes of the hyperbola \( \frac{x^2}{4} - \frac{y^2}{9} = 1 \) are:
    • A) \( y = \pm \frac{3}{2}x \) (Answer)
    • B) \( y = \pm \frac{2}{3}x \)
    • C) \( y = \pm 3x \)
    • D) \( y = \pm 2x \)
43. The conjugate axis of the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \) is of length:
    • A) 6 (Answer)
    • B) 8
    • C) 12
    • D) 4
44. The equation of a circle passing through the origin and having the line \( x + y = 4 \) as a diameter is:
    • A) \( x^2 + y^2 - 4x - 4y = 0 \)
    • B) \( x^2 + y^2 - 4x - 4y + 8 = 0 \) (Answer)
    • C) \( x^2 + y^2 + 4x + 4y - 8 = 0 \)
    • D) \( x^2 + y^2 - 4x - 4y - 8 = 0 \)
45. The center of the conic section \( 3x^2 - 4xy + y^2 - 2x + 4y - 1 = 0 \) is:
    • A) (-2, 1)
    • B) (1, 2) (Answer)
    • C) (2, -1)
    • D) (-1, -2)

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