JEE (Main) Mathematics - CO-ORDINATE GEOMETRY Multiple Choice Questions (MCQs) with Answers

46. The equation of the line passing through the point (2, 5) and parallel to the line 3x + 4y - 10 = 0 is:

A) 3x + 4y - 14 = 0 (Correct Answer)
B) 3x + 4y - 15 = 0
C) 3x + 4y - 16 = 0
D) 3x + 4y - 13 = 0

47. The equation of the line passing through the point (1, 2) and perpendicular to the line x - y = 3 is:

A) x + y = 3
B) x - y = 0
C) x + y = 1 (Correct Answer)
D) x - y = 2

48. The distance between the point (3, -4) and the line 2x + 3y - 10 = 0 is:

A) 2
B) 3 (Correct Answer)
C) 1
D) 4

49. The coordinates of the centroid of the triangle with vertices (0, 0), (4, 0), and (0, 6) are:

A) (2, 2)
B) (1, 1)
C) (4, 6)
D) (2, 1) (Correct Answer)

50. The equation of the circle with center at (2, 3) and radius 5 is:

A) (x - 2)^2 + (y - 3)^2 = 25 (Correct Answer)
B) (x - 2)^2 + (y + 3)^2 = 25
C) (x + 2)^2 + (y - 3)^2 = 25
D) (x + 2)^2 + (y + 3)^2 = 25

51. The equation of a circle with the endpoints of the diameter at (1, 2) and (5, 6) is:

A) (x - 3)^2 + (y - 4)^2 = 10 (Correct Answer)
B) (x + 3)^2 + (y - 4)^2 = 10
C) (x - 3)^2 + (y + 4)^2 = 10
D) (x + 3)^2 + (y + 4)^2 = 10

52. The equation of the ellipse with a major axis of 10 and a minor axis of 8 is:

A) (x^2 / 25) + (y^2 / 16) = 1 (Correct Answer)
B) (x^2 / 16) + (y^2 / 25) = 1
C) (x^2 / 10) + (y^2 / 8) = 1
D) (x^2 / 8) + (y^2 / 10) = 1

53. The equation of the parabola with vertex at (0, 0) and focus at (0, -2) is:

A) x^2 = -8y
B) y^2 = -8x
C) x^2 = 4y
D) y^2 = 4x (Correct Answer)

54. The equation of the hyperbola with transverse axis 10 and conjugate axis 8 is:

A) (x^2 / 25) - (y^2 / 16) = 1 (Correct Answer)
B) (x^2 / 16) - (y^2 / 25) = 1
C) (x^2 / 16) - (y^2 / 8) = 1
D) (x^2 / 8) - (y^2 / 16) = 1

55. The equation of the circle with center at (4, 5) and radius 3 is:

A) (x - 4)^2 + (y - 5)^2 = 9 (Correct Answer)
B) (x + 4)^2 + (y - 5)^2 = 9
C) (x - 4)^2 + (y + 5)^2 = 9
D) (x + 4)^2 + (y + 5)^2 = 9

56. The eccentricity of the ellipse \( \frac{x^2}{36} + \frac{y^2}{16} = 1 \) is:

A) \( \frac{4}{5} \) (Correct Answer)
B) \( \frac{5}{4} \)
C) \( \frac{3}{4} \)
D) \( \frac{5}{3} \)

57. The equation of the circle passing through the origin and having center (1, 1) is:

A) x^2 + y^2 - 2x - 2y = 0 (Correct Answer)
B) x^2 + y^2 - x - y = 0
C) x^2 + y^2 + 2x + 2y = 0
D) x^2 + y^2 + x + y = 0

58. The equation of the line passing through the point (3, 4) and making an angle of \( \frac{\pi}{4} \) with the positive x-axis is:

A) y - 4 = x - 3 (Correct Answer)
B) y + 4 = x + 3
C) y - 4 = 2(x - 3)
D) y - 4 = -x + 3

59. The equation of the straight line passing through the origin and making an angle of 45 degrees with the positive x-axis is:

A) y = x (Correct Answer)
B) y = -x
C) y = 2x
D) y = 3x

60. The equation of the ellipse with foci at (0, ±4) and major axis of length 8 is:

A) \( \frac{x^2}{16} + \frac{y^2}{4} = 1 \) (Correct Answer)
B) \( \frac{x^2}{4} + \frac{y^2}{16} = 1 \)
C) \( \frac{x^2}{8} + \frac{y^2}{4} = 1 \)
D) \( \frac{x^2}{4} + \frac{y^2}{8} = 1 \)

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