MCQ in Analytic Geometry: Points, Lines and Circles Part 2 – Answers

MCQ in Analytic Geometry: Points, Lines and Circles Part 2 Answer Key | Mathematics Board Exam

Part 2 is done. Now use this answer key to get an honest picture of where your review actually stands.

Every answer in this set comes from past board exam problems, engineering mathematics textbooks, academic journals, and other dependable references used by reviewees preparing for the Mathematics section of the board exam. This is not just a tool for checking correct answers. It is a way to measure how well your understanding of points, lines and circles has developed since Part 1 and to identify what still needs work before exam day.

By Part 2, the problems are testing more than just formula recall. They are checking whether you can apply analytic geometry concepts correctly when the question is framed in a way that is slightly different from what you practiced before. If certain items in this set gave you more trouble than expected, pay close attention to those. They are telling you exactly where the gaps are.

Go through every answer in this set with full honesty. For each wrong item, trace the complete solution and find where your reasoning broke down. Was it the setup? The formula you reached for? The way you interpreted the problem? Understanding the source of each mistake is the only way to make sure the same error does not show up again on the actual exam.

Part 1 answer key is still on Pinoybix if you need to revisit anything from the first set. Take what you learned from this review and carry that focus into Part 3.

51. B. IV

52. C. IV

53. C. (11, -20)

Solution: The terminal point is

54. C. (6, -6)

Solution: Find the coordinate of P1

55. B. (1, 1)

Solution: Find the coordinates of the point P(2,4) with respect to the translated axis

56. C. 5

Solution: Find the median through (-2, -5) of the triangle

57. A. (0, 1)

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

58. C. 38

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

59. D. 9.487

Solution: Find the distance between the points (4, -2) and (-5, 1)

60. D. 10

Solution: Find the distance between A(4, -3) and B(-2, 5)

61. C. 19 or –5

Solution: What is the value of y?

62. B. √2

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

63. B. 5.4

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

64. B. 2.36

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

65. C. 3

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

66. B. 3.54

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

67. D. (64, -44) and (4, -4)

Solution: The two points on the lines 2x + 3y +4 = 0 which are at distance 2

68. D. (x/a) + (y/b) = 1

69. A. 1

Solution: Find the slope of the line defined by y – x = 5

70. B. -3/2

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

71. B. –3

Solution: Find the slope of the line whose parametric equation

72. A. 2

Solution: Find the slope of the curve whose parametric equations

73. D. 77.47°

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

74. C. 3x – 4y – 5 = 0

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

75. A. 4y = 1

Solution: Find the equation of the bisector of the obtuse angle between the lines

76. A. 3x – 2y + 1 = 0

Solution: The equation of the line through (1, 2) and parallel to the line

77. D. 3x – 2y – 1 = 0

Solution: Which of the following is correct?

78. B. 45°

Solution: The acute angle between the two lines is

79. B. Are coincident

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

80. B. 5x – 4y – 1 = 0

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

81. B. y = 2x – 3

Solution: Find the equation of the line with slope of 2 and y-intercept of -3

82. B. y – x + 4 = 0

Solution: What is the equation of the line that passes through (4, 0) and is parallel to the line

83. B. 3

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

84. C. 3x – 2y = 12

Solution: The equation of a line that intercepts the x-axis at x = 4 and the y-axis

85. D. 2.5

Solution: How far from the y-axis is the center of the curve 2x^2 + 2y^2 + 10x – 6y – 55 = 0?

86. B. 9π

Solution: Find the area of the circle whose center is at (2,-5) and tangent to the line

87. B. 225π

Solution: Determine the area enclosed by the curve x^2 – 10x + 4y + y^2 = 196

88. C. 5.81

Solution: Find the shortest distance from the point (1, 2) to a point on the circumference of the circle

89. A. 13.86

Solution: Determine the length of the chord common to the circles

90. B. 25π

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

91. A. (√33)/4

Solution: The radius of the circle 2x^2 + 2y^2 – 3x + 4y – 1 = 0  is

92. B. 5

Solution: What is the radius of the circle with the following equation?

93. D. 8/3

Solution: The diameter of a circle described by 9x^2 + 9y^2  = 16

94. A. (3, -2)

Solution: Find the center of the circle x^2 + y^2 – 6x + 4y – 23 = 0

95. C. x² + y² – 8x – 10y + 25 = 0

Solution: Determine the equation of the circle whose center is at (4, 5) and tangent to the circle 

96. A. x² + y² + 4x – 6y – 12 = 0

Solution: The equation of the circle with center at (-2, 3) and which is tangent to the line

97. B. 4x² + 4y² – 36x + 16y – 192 = 0

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

98. C. x² + y² + 6x – 14y + 49 = 0

Solution: Find the equation of the circle with center on x + y = 4 and 5x + 2y + 1 = 0 

99. A. x² + y² + 2x – 2y – 23 = 0

100. B. -5

Solution: Find the equation of k for which the equation x^2 + y^2 + 4x – 2y – k = 0 

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: