JEE Main Mathematics: Coordinate Geometry MCQs

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JEE (Main) Mathematics - CO-ORDINATE GEOMETRY MCQs

61. The distance between the points (2, 3) and (5, 7) is:

A) \( \sqrt{29} \)
B) \( \sqrt{34} \) (Correct Answer)
C) \( \sqrt{25} \)
D) 5

62. The midpoint of the line joining the points (4, -3) and (-2, 5) is:

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

63. The equation of a line passing through the point (2, 3) and having a slope of 4 is:

A) \( y - 3 = 4(x - 2) \) (Correct Answer)
B) \( y - 2 = 4(x - 3) \)
C) \( y = 4x - 1 \)
D) \( y - 3 = 2(x - 4) \)

64. The equation of the line that passes through the origin and has a slope of 3 is:

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

65. The slope of the line passing through the points (-1, 4) and (3, 7) is:

A) 3/4
B) 1/4
C) 3/5
D) 3/2 (Correct Answer)

66. The point of intersection of the lines \( 2x + 3y = 10 \) and \( x - y = 3 \) is:

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

67. The equation of the line whose x-intercept is 4 and y-intercept is 3 is:

A) \( x + y = 7 \)
B) \( 3x + 4y = 12 \)
C) \( \frac{x}{4} + \frac{y}{3} = 1 \) (Correct Answer)
D) \( x - y = 1 \)

68. The distance from the point (3, 4) to the line \( 2x + 3y - 5 = 0 \) is:

A) 1
B) 2
C) 3
D) \( \frac{1}{\sqrt{13}} \) (Correct Answer)

69. The coordinates of the centroid of the triangle with vertices at (1, 2), (3, 4), and (5, 6) are:

A) (3, 4)
B) (3, 3)
C) (2, 3) (Correct Answer)
D) (4, 5)

70. The equation of the circle with center (0, 0) and radius 5 is:

A) \( x^2 + y^2 = 5 \)
B) \( x^2 + y^2 = 25 \) (Correct Answer)
C) \( x^2 + y^2 = 10 \)
D) \( x^2 + y^2 = 20 \)

71. The equation of the circle with diameter endpoints at (1, 1) and (5, 5) is:

A) \( (x - 3)^2 + (y - 3)^2 = 8 \) (Correct Answer)
B) \( (x - 3)^2 + (y - 3)^2 = 16 \)
C) \( (x - 2)^2 + (y - 2)^2 = 4 \)
D) \( x^2 + y^2 - 6x - 6y = 8 \)

72. The equation of the parabola with vertex at (0, 0) and focus at (0, 4) is:

A) \( x^2 = 16y \)
B) \( y^2 = 16x \)
C) \( x^2 = 4y \)
D) \( y^2 = 4x \) (Correct Answer)

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

A) \( \frac{x^2}{16} + \frac{y^2}{9} = 1 \)
B) \( \frac{x^2}{64} + \frac{y^2}{16} = 1 \)
C) \( \frac{x^2}{64} + \frac{y^2}{36} = 1 \) (Correct Answer)
D) \( \frac{x^2}{9} + \frac{y^2}{16} = 1 \)

74. The area of the triangle formed by the lines \( x + y = 4 \), \( x - y = 2 \), and \( x = 0 \) is:

A) 4
B) 3
C) 5 (Correct Answer)
D) 6

75. The area of the quadrilateral with vertices at (1, 2), (3, 4), (5, 6), and (7, 8) is:

A) 8
B) 10
C) 12
D) 0 (Correct Answer)

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