MCQ in Analytic Geometry: Points, Lines and Circles Part 2 | Math Board Exam

(Last Updated On: January 3, 2021)

MCQs in Analytic Geometry: Points, Lines and Circles Part 2

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.

MCQ Topic Outline included in Mathematics Board Exam Syllabi

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

Continue Practice Exam Test Questions Part 2 of the Series

MCQ in Analytic Geometry: Points, Lines and Circles Part 1 | Math Board Exam

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

View Answer:

Answer: Option B

Solution:

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

A. III

B. I

C. IV

D. II

View Answer:

Answer: Option C

Solution:

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)

View Answer:

Answer: Option C

Solution:

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

A. (6, -5)

B. (5, -6)

C. (6, -6)

D. (-6, 6)

View Answer:

Answer: Option C

Solution:

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)

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option C

Solution:

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)

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option C

Solution:

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

A. 4.897

B. 8.947

C. 7.149

D. 9.487

View Answer:

Answer: Option D

Solution:

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

A. 11

B. 8

C. 9

D. 10

View Answer:

Answer: Option D

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option B

Solution:

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

A. 1

B. 2

C. 3

D. 4

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option B

Solution:

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)

View Answer:

Answer: Option D

Solution:

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

View Answer:

Answer: Option D

Solution:

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

A. 1

B. -1/2

C. ¼

D. 5 + x

View Answer:

Answer: Option A

Solution:

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

A. -2/3

B. -3/2

C. 3/2

D. 2/3

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option B

Solution:

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

x = -1 + t

y = 2t

A. 2

B. 3

C. 1

D. 4

View Answer:

Answer: Option A

Solution:

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°

View Answer:

Answer: Option D

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option D

Solution:

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°

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option C

Solution:

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

A. 2

B. 3

C. 4

D. 5

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option C

Solution:

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

A. -3.0

B. 2.75

C. -3.25

D. 2.5

View Answer:

Answer: Option D

Solution:

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

View Answer:

Answer: Option A

Solution:

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

A. 15π

B. 225π

C. 12π

D. 144π

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option B

Solution:

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

A. (√33)/4

B. 33/16

C. (√33)/3

D. 17

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option B

Solution:

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

A. 16/9

B. 4/3

C. 4

D. 8/3

View Answer:

Answer: Option D

Solution:

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)

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option B

Solution:

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

Following is the list of practice exam test questions s in this brand new series:

MCQ in Analytic Geometry: Points, Lines and Circles
PART 1: MCQ from Number 1 – 50                             Answer key: PART 1
PART 2: MCQ from Number 51 – 100                        Answer key: PART 2

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