MCQs in Analytic Geometry: Points, Lines and Circles Part II

This is the Multiple Choice Questions Part 2 of the Series in Analytic Geometry: Points, Lines and Circles topics in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

Multiple Choice Questions Topic Outline

• MCQs in Rectangular coordinates system | MCQs in Distance Formula | MCQs in Distance between two points in space | MCQs in Slope of a Line | MCQs in Angle between two lines| MCQs in Distance between a point and a line | MCQs in Distance between two lines | MCQs in Division of line segment | MCQs in Area by coordinates | MCQs in Lines | MCQs in Conic sections | MCQs in Circles

Online Questions and Answers in Analytic Geometry: Points, Lines and Circles Series

Following is the list of multiple choice questions in this brand new series:

Analytic Geometry: Points, Lines and Circles MCQs

PART 1: MCQs from Number 1 – 50                        Answer key: PART I

PART 2: MCQs from Number 51 – 100                        Answer key: PART II

Continue Practice Exam Test Questions Part II of the Series

Choose the letter of the best answer in each questions.

51. State the quadrant in which the coordinate (15, -2) lies.

• A. I
• B. IV
• C. II
• D. III

52. Of what quadrant is A, if sec A is positive and csc A is negative?

• A. III
• B. I
• C. IV
• D. II

53. The segment from (-1, 4) to (2, -2) is extended three times its own length. The terminal point is

• A. (11, -18)
• B. (11, -24)
• C. (11, -20)
• D. (-11, -20)

54. The midpoint of the line segment between P₁(x, y) and P₂(-2, 4) is P_m(2, -1). Find the coordinate of P₁.

• A. (6, -5)
• B. (5, -6)
• C. (6, -6)
• D. (-6, 6)

55. Find the coordinates of the point P(2,4) with respect to the translated axis with origin at (1,3).

• A. (1, -1)
• B. (1, 1)
• C. (-1, -1)
• D. (-1, 1)

56. Find the median through (-2, -5) of the triangle whose vertices are (-6, 2), (2, -2), and (-2, -5).

• A. 3
• B. 4
• C. 5
• D. 6

57. Find the centroid of a triangle whose vertices are (2, 3), (-4, 6) and (2, -6).

• A. (0, 1)
• B. (0, -1)
• C. (1, 0)
• D. (-1, 0)

58. Find the area of triangle whose vertices are A (-3, -1), B(5, 3) and (2, -8)

• A. 34
• B. 36
• C. 38
• D. 32

59. Find the distance between the points (4, -2) and (-5, 1)

• A. 4.897
• B. 8.947
• C. 7.149
• D. 9.487

60. Find the distance between A(4, -3) and B(-2, 5).

• A. 11
• B. 8
• C. 9
• D. 10

61. If the distance between the points (8, 7) and (3, y) is 13, what is the value of y?

• A. 5
• B. -19
• C. 19 or -5
• D. 5 or -19

62. The distance between the points (sin x, cos x) and (cos x, -sin x) is:

• A. 1
• B. √2
• C. 2 sin x cos x
• D. 4 sin x cos x

63. Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0.

• A. 5
• B. 5.4
• C. 5.8
• D. 6.2

64. Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0.

• A. 2.62
• B. 2.36
• C. 2.48
• D. 2.54

65. How far is the line 3x – 4y + 15 = 0 from the origin?

• A. 1
• B. 2
• C. 3
• D. 4

66. Determine the distance from (5, 10) to the line x – y = 0

• A. 3.86
• B. 3.54
• C. 3.68
• D. 3.72

67. The two points on the lines 2x + 3y +4 = 0 which are at distance 2 from the line 3x + 4y – 6 = 0 are:

• A. (-8, -8) and (-16, -16)
• B. (-44, 64) and (-5, 2)
• C. (-5.5, 1) and (-5, 2)
• D. (64, -44) and (4, -4)

68. The intercept form for algebraic straight-line equation is:

• A. (a/x) + (y/b) = 1
• B. y = mx + b
• C. Ax + By + C = 0
• D. (x/a) + (y/b) = 1

69. Find the slope of the line defined by y – x = 5

• A. 1
• B. -1/2
• C. ¼
• D. 5 + x

70. The slope of the line 3x + 2y + 5 = 0 is:

• A. -2/3
• B. -3/2
• C. 3/2
• D. 2/3

71. Find the slope of the line whose parametric equation is y = 5 – 3t and x = 2 + t.

• A. 3
• B. -3
• C. 2
• D. -2

72. Find the slope of the curve whose parametric equations are

x = -1 + t

y = 2t

• A. 2
• B. 3
• C. 1
• D. 4

73. Find the angle that the line 2y – 9x – 18 = 0 makes with the x-axis.

• A. 74.77°
• B. 4.5°
• C. 47.77°
• D. 77.47°

74. Which of the following is perpendicular to the line x/3 + y/4 = 1?

• A. x – 4y – 8 = 0
• B. 4x – 3y – 6 = 0
• C. 3x – 4y – 5 = 0
• D. 4x + 3y – 11 = 0

75. Find the equation of the bisector of the obtuse angle between the lines 2x + y = 4 and 4x - 2y = 7

• A. 4y = 1
• B. 8x = 15
• C. 2y = 3
• D. 8x + 4y = 6

76. The equation of the line through (1, 2) and parallel to the line 3x – 2y + 4 = 0 is:

• A. 3x – 2y + 1 = 0
• B. 3x – 2y – 1 = 0
• C. 3x + 2y + 1 = 0
• D. 3x + 2y – 1 = 0

77. If the points (-3, -5), (x, y), and (3, 4) lie on a straight line, which of the following is correct?

• A. 3x + 2y – 1 = 0
• B. 2x + 3y + 1 = 0
• C. 2x + 3y – 1 = 0
• D. 3x – 2y – 1 = 0

78. One line passes through the points (1, 9) and (2, 6), another line passes through (3, 3) and (-1, 5). The acute angle between the two lines is:

• A. 30°
• B. 45°
• C. 60°
• D. 135°

79. The two straight lines 4x – y + 3 = 0 and 8x – 2y + 6 = 0

• A. Intersects at the origin
• B. Are coincident
• C. Are parallel
• D. Are perpendicular

80. A line which passes through (5, 6) and (-3. -4) has an equation of

• A. 5x + 4y + 1 = 0
• B. 5x - 4y - 1 = 0
• C. 5x - 4y + 1 = 0
• D. 5x + y - 1 = 0

81. Find the equation of the line with slope of 2 and y-intercept of -3.

• A. y = -3x + 2
• B. y = 2x – 3
• C. y = 2/3 x + 1
• D. y = 3x – 2

82. What is the equation of the line that passes through (4, 0) and is parallel to the line x – y – 2 = 0?

• A. y + x + 4 = 0
• B. y - x + 4 = 0
• C. y - x - 4 = 0
• D. y + x - 4 = 0

83. Determine B such that 3x + 2y – 7 = 0 is perpendicular to 2x – By + 2 = 0

• A. 2
• B. 3
• C. 4
• D. 5

84. The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = -6 is:

• A. 2x – 3y = 12
• B. 3x + 2y = 12
• C. 3x – 2y = 12
• D. 2x – 37 = 12

85. How far from the y-axis is the center of the curve 2x² + 2y² + 10x – 6y – 55 = 0?

• A. -3.0
• B. 2.75
• C. -3.25
• D. 2.5

86. Find the area of the circle whose center is at (2,-5) and tangent to the line 4x + 3y – 8 = 0.

• A. 6π
• B. 9π
• C. 3π
• D. 12π

87. Determine the area enclosed by the curve x² – 10x + 4y + y² = 196

• A. 15π
• B. 225π
• C. 12π
• D. 144π

88. Find the shortest distance from the point (1, 2) to appoint on the circumference of the circle defined by the equation x² + y² + 10x + 6y + 30 = 0.

• A. 5.61
• B. 5.71
• C. 5.81
• D. 5.91

89. Determine the length of the chord common to the circles x² + y² = 64 and x² + y² – 16x – 0.

• A. 13.86
• B. 12.82
• C. 13.25
• D. 12.28

90. If (3, -2) is on a circle with center (-1, 1), then the area of the circle is:

• A. 5π
• B. 25π
• C. 4π
• D. 3π

91. The radius of the circle 2x² + 2y² – 3x + 4y – 1 = 0  is:

• A. (√33)/4
• B. 33/16
• C. (√33)/3
• D. 17

92. What is the radius of the circle with the following equation?

x² – 6x + y² – 4y – 12 = 0

• A. 3.46
• B. 5
• C. 7
• D. 6

93. The diameter of a circle described by 9x² + 9y²  = 16  is:

• A. 16/9
• B. 4/3
• C. 4
• D. 8/3

94. Find the center of the circle x² + y² – 6x + 4y – 23 = 0.

• A. (3, -2)
• B. (3, 2)
• C. (-3, 2)
• D. (-3, -2)

95. Determine the equation of the circle whose center is at (4, 5) and tangent to the circle whose equation is x² + y² + 4x + 6y – 23 = 0.

• A. x² + y² – 8x + 10y – 25 = 0
• B. x² + y² + 8x – 10y + 25 = 0
• C. x² + y² – 8x – 10y + 25 = 0
• D. x² + y² – 8x – 10y – 25 = 0

96. The equation of the circle with center at (-2, 3) and which is tangent to the line 20x – 21y – 42 = 0.

• A. x² + y² + 4x – 6y – 12 = 0
• B. x² + y² + 4x – 6y + 12 = 0 
• C. x² + y² + 4x + 6y – 12 = 0 
• D. x² + y² – 4x – 6y – 12 = 0 

97. A circle has a diameter whose ends are at (-3, 2) and (12, -6). Its Equation is:

• A. 4x² + 4y² – 36x + 16y + 192 = 0 
• B. 4x² + 4y² – 36x + 16y – 192 = 0
• C. 4x² + 4y² – 36x – 16y – 192 = 0
• D. 4x² + 4y² – 36x – 16y + 192 = 0

98. Find the equation of the circle with center on x + y = 4 and 5x + 2y + 1 = 0 and having a radius of 3.

• A. x² + y² + 6x – 16y + 64 = 0 
• B. x² + y² + 8x – 14y + 25 = 0
• C. x² + y² + 6x – 14y + 49 = 0
• D. x² + y² + 6x – 14y + 36 = 0

99. If (3, -2) lies on the circle with center (-1, 1) then the equation of the circle is:

• A. x² + y² + 2x – 2y – 23 = 0 
• B. x² + y² + 4x – 2y – 21 = 0
• C. x² + y² + 2x – y – 33 = 0
• D. x² + y² + 4x – 2y – 27 = 0

100. Find the equation of k for which the equation x² + y² + 4x – 2y – k = 0   represents a point circle.

• A. 5
• B. -5
• C. 6
• D. -6

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