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MCQ in Analytic Geometry: Parabola, Ellipse and Hyperbola Part 2 | Math Board Exam

MCQ in Analytic Geometry: Parabola, Ellipse and Hyperbola Part 2

This is the Multiple Choice Questions Part 2 of the Series in Analytic Geometry: Parabola, Ellipse and Hyperbola 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: Parabola, Ellipse and Hyperbola Part 1 | Math Board Exam

Choose the letter of the best answer in each questions.

51. The vertex of the parabola y2 – 2x + 6y + 3 = 0 is at:

A. (-3, 3)

B. (3, 3)

C. (-3, 3)

D. (-3, -3)

View Answer:

Answer: Option D

Solution:

52. The length of the latus rectum of the parabola y2 = 4px is:

A. 4p

B. 2p

C. P

D. -4p

View Answer:

Answer: Option A

Solution:

53. Given the equation of the parabola:  y2 – 8x – 4y – 20  = 0. The length of its latus rectum is:

A. 2

B. 4

C. 6

D. 8

View Answer:

Answer: Option D

Solution:

54. What is the length of the latus rectum of the curve x2 = –12y?

A. 12

B. -3

C. 3

D. -12

View Answer:

Answer: Option A

Solution:

55. Find the equation of the directrix of the parabola y2 = 6x.

A. x = 8

B. x = 4

C. x = -8

D. x = -4

View Answer:

Answer: Option D

Solution:

56. The curve y = –x2 + x + 1 opens:

A. Upward

B. To the left

C. To the right

D. Downward

View Answer:

Answer: Option D

Solution:

57. The parabola y = –x2 + x + 1 opens:

A. To the right

B. To the left

C. Upward

D. Downward

View Answer:

Answer: Option D

Solution:

58. Find the equation of the axis of symmetry of the function y = 2x2 – 7x + 5.

A. 4x + 7 = 0

B. x – 2 = 0

C. 4x – 7 = 0

D. 7x + 4 = 0

View Answer:

Answer: Option C

Solution:

59. Find the equation of the locus of the center of the circle which moves so that it is tangent to the y-axis and to the circle of radius one (1) with center at (2,0).

A. x2 + y2 – 6x + 3 = 0

B. x2 – 6x + 3 = 0

C. 2x2 + y2 – 6x + 3 = 0

D. y2 – 6x + 3 = 0

View Answer:

Answer: Option D

Solution:

60. Find the equation of the parabola with vertex at (4, 3) and focus at (4, -1).

A. y2 – 8x + 16y – 32 = 0

B. y2 + 8x + 16y – 32 = 0

C. y2 + 8x – 16y + 32 = 0

D. x2 – 8x + 16y – 32 = 0

View Answer:

Answer: Option D

Solution:

61. Find the area bounded by the curves x2 + 8y + 16 = 0, x – 4 = 0, the x-axis, and the y-axis.

A. 10.67 sq. units

B. 10.33 sq. units

C. 9.67 sq. units

D. 8 sq. units

View Answer:

Answer: Option A

Solution:

62. Find the area (in sq. units) bounded by the parabolas x2 – 2y = 0  and x2 + 2y – 8 = 0

A. 11.7

B. 10.7

C. 9.7

D. 4.7

View Answer:

Answer: Option B

Solution:

63. The length of the latus rectum of the curve (x – 2)2 / 4 = (y + 4)2 / 25 = 1 is:

A. 1.6

B. 2.3

C. 0.80

D. 1.52

View Answer:

Answer: Option A

Solution:

64. Find the length of the latus rectum of the following ellipse:

25x2 + 9y2 – 300x –144y + 1251 = 0

A. 3.4

B. 3.2

C. 3.6

D. 3.0

View Answer:

Answer: Option C

Solution:

65. If the length of the major and minor axes of an ellipse is 10 cm and 8 cm, respectively, what is the eccentricity of the ellipse?

A. 0.50

B. 0.60

C. 0.70

D. 0.80

View Answer:

Answer: Option B

Solution:

66. The eccentricity of the ellipse x2/4 + y2 / 16 = 1 is:

A. 0.725

B. 0.256

C. 0.689

D. 0.866

View Answer:

Answer: Option D

Solution:

67. An ellipse has the equation 16x2 + 9y2 + 32x – 128 = 0. Its eccentricity is:

A. 0.531

B. 0.66

C. 0.824

D. 0.93

View Answer:

Answer: Option B

Solution:

68. The center of the ellipse 4x2 + y2 – 16x – 6y – 43 = 0 is at:

A. (2, 3)

B. (4, -6)

C. (1, 9)

D. (-2, -5)

View Answer:

Answer: Option A

Solution:

69. Find the ratio of the major axis to the minor axis of the ellipse:

9x2 + 4y2 – 72x – 24y – 144 = 0

A. 0.67

B. 1.8

C. 1.5

D. 0.75

View Answer:

Answer: Option C

Solution:

70. The area of the ellipse 9x2 + 25y2 – 36x  – 189 = 0 is equal to:

A. 15π sq. units

B. 20π sq. units

C. 25π sq. units

D. 30π sq. units

View Answer:

Answer: Option A

Solution:

71. The area of the ellipse is given as A = 3.1416 a b. Find the area of the ellipse 25x2 + 16y2 – 100x  + 32y = 284

A. 86.2 square units

B. 62.8 square units

C. 68.2 square units

D. 82.6 square units

View Answer:

Answer: Option B

Solution:

72. The semi-major axis of an ellipse is 4 and its semi-minor axis is 3. The distance from the center to the directrix is:

A. 6.532

B. 6.047

C. 0.6614

D. 6.222

View Answer:

Answer: Option B

Solution:

73. Given an ellipse x2 / 36 + y2 / 32 = 1. Determine the distance between foci.

A. 2

B. 3

C. 4

D. 8

View Answer:

Answer: Option C

Solution:

74. How far apart are the directrices of the curve 25x2 + 9y2 – 300x – 144y + 1251 = 0?

A. 12.5

B. 14.2

C. 13.2

D. 15.2

View Answer:

Answer: Option A

Solution:

75. The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth.

A. 94,550,000 miles

B. 94,335.100 miles

C. 91,450,000 miles

D. 93,000,000 miles

View Answer:

Answer: Option A

Solution:

76. Find the equation of the ellipse whose center is at (-3, -1), vertex at (2, -1), and focus at (1, -1).

A. 9x2 + 36y2 – 54x + 50y – 116 = 0

B. 4x2 + 25y2 + 54x – 50y – 122 = 0

C. 9x2 + 25y2 + 50x + 50y + 109 = 0

D. 9x2 + 25y2 + 54x + 50y – 119 = 0

View Answer:

Answer: Option D

Solution:

77. Point P(x, y) moves with a distance from point (0, 1) one-half of its distance from line y = 4, the equation of its locus is

A. 4x2 + 3y2 = 12

B. 2x2 – 4y2 = 5

C. x2 + 2y2 = 4

D. 2x2 + 5y3 = 3

View Answer:

Answer: Option A

Solution:

78. The chords of the ellipse 642 + 25y2 = 1600 having equal slopes of 1/5 are bisected by its diameter. Determine the equation of the diameter of the ellipse.

A. 5x – 64y = 0

B. 64x – 5y = 0

C. 5x +64y = 0

D. 64x + 5y = 0

View Answer:

Answer: Option D

Solution:

79. Find the equation of the upward asymptote of the hyperbola whose equation is (x – 2)2 / 9 – (y + 4)2 / 16

A. 3x + 4y – 20 = 0

B. 4x – 3y – 20 = 0

C. 4x + 3y – 20 = 0

D. 3x – 4y – 20 = 0

View Answer:

Answer: Option B

Solution:

80. The semi-conjugate axis of the hyperbola (x2/9) – (y2/4) = 1 is:

A. 2

B. -2

C. 3

D. -3

View Answer:

Answer: Option A

Solution:

81. What is the equation of the asymptote of the hyperbola (x2/9) – (y2/4) = 1.

A. 2x – 3y = 0

B. 3x – 2y = 0

C. 2x – y = 0

D. 2x + y = 0

View Answer:

Answer: Option A

Solution:

82. The graph y = (x – 1) / (x + 2) is not defined at:

A. 0

B. 2

C. -2

D. 1

View Answer:

Answer: Option C

Solution:

83. The equation x2 + Bx + y2 + Cy + D = 0 is:

A. Hyperbola

B. Parabola

C. Ellipse

D. Circle

View Answer:

Answer: Option D

Solution:

84. The general second degree equation has the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 and describes an ellipse if:

A. B2 – 4AC = 0

B. B2 – 4AC > 0

C. B2 – 4AC = 1

D. B2 – 4AC < 0

View Answer:

Answer: Option D

Solution:

85. Find the equation of the tangent to the circle x2 + y2 – 34 = 0 through point (3, 5).

A. 3x + 5y -34 = 0

B. 3x – 5y – 34 = 0

C. 3x + 5y + 34 = 0

D. 3x – 5y + 34 = 0

View Answer:

Answer: Option A

Solution:

86. Find the equation of the tangent to the curve x2 + y2 + 4x + 16y – 32 = 0 through (4, 0).

A. 3x – 4y + 12 = 0

B. 3x – 4y – 12 = 0

C. 3x + 4y + 12 = 0

D. 3x + 4y – 12 = 0

View Answer:

Answer: Option D

Solution:

87. Find the equation of the normal to the curve y2 + 2x + 3y = 0 though point (-5,2)

A. 7x + 2y + 39 = 0

B. 7x – 2y + 39 = 0

C. 2x – 7y – 39 = 0

D. 2x + 7y – 39 = 0

View Answer:

Answer: Option B

Solution:

88. Determine the equation of the line tangent to the graph y = 2x2 + 1, at the point (1, 3).

A. y = 4x + 1

B. y = 4x – 1

C. y = 2x – 1

D. y = 2x + 1

View Answer:

Answer: Option B

Solution:

89. Find the equation of the tangent to the curve x2 + y2 = 41 through (5, 4).

A. 5x + 4y = 41

B. 4x – 5y = 41

C. 4x + 5y = 41

D. 5x – 4y = 41

View Answer:

Answer: Option A

Solution:

90. Find the equation of a line normal to the curve x2 = 16y at (4, 1).

A. 2x – y – 9 = 0

B. 2x – y + 9 =

C. 2x + y – 9 = 0

D. 2x + y + 9 = 0

View Answer:

Answer: Option C

Solution:

91. What is the equation of the tangent to the curve 9x2 + 25y2 – 225 = 0 at (0, 3)?

A. y + 3 = 0

B. x + 3 = 0

C. x – 3 = 0

D. y – 3 = 0

View Answer:

Answer: Option D

Solution:

92. What is the equation of the normal to the curve x2 + y2 = 25 at (4, 3)?

A. 3x – 4y = 0

B. 5x + 3y = 0

C. 5x – 3y = 0

D. 3x + 4y = 0

View Answer:

Answer: Option A

Solution:

93. The polar form of the equation 3x + 4y – 2 = 0 is:

A. 3r sin Ѳ + 4r cos Ѳ = 2

B. 3r cos Ѳ + 4r sin Ѳ = -2

C. 3r cos Ѳ + 4r sin Ѳ = 2

D. 3r sin Ѳ + 4r tan Ѳ = -2

View Answer:

Answer: Option C

Solution:

94. The polar form of the equation 3x + 4y – 2 = 0 is:

A. r2 = 8

B. r = Ѳ/(cos2 Ѳ + 2)

C. r = 8

D. r2 = 8/(cos2 Ѳ + 2)

View Answer:

Answer: Option D

Solution:

95. the distance between points (5, 30°) and (-8, -50°) is:

A. 9.84

B. 10.14

C. 6.13

D. 12.14

View Answer:

Answer: Option B

Solution:

96. Convert Ѳ = π/3  to Cartesian equation.

A. x = √3 x

B. y = x

C. 3y = √3 x

D. y =√3 x

View Answer:

Answer: Option D

Solution:

97. The point of intersection of the planes x + 5y – 2z = 9, 3x – 2y + z = 3, and x + y + z = 2 is:

A. (2, 1, -1)

B. (2, 0, -1)

C. (-1, 1, -1)

D. (-1, 2, 1)

View Answer:

Answer: Option A

Solution:

98. A warehouse roof needs a rectangular skylight with vertices (3, 0, 0), (3, 3, 0), (0, 3, 4), and (0, 0, 4). If the units are in meter, the area of the skylight is:

A. 12 sq. m.

B. 20 sq. m.

C. 15 sq. m.

D. 9 sq. m.

View Answer:

Answer: Option C

Solution:

99. The distance between points in space coordinates are (3, 4, 5) and (4, 6, 7) is:

A. 1

B. 2

C. 3

D. 4

View Answer:

Answer: Option C

Solution:

100. What is the radius of the sphere with center at origin and which passes through the point (8, 1, 6)?

A. 10

B. 9

C.√101

D. 10.5

View Answer:

Answer: Option C

Solution:

Online Questions and Answers in Analytic Geometry: Parabola, Ellipse and Hyperbola Series

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

MCQ in Analytic Geometry: Parabola, Ellipse and Hyperbola
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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