MCQs in Analytic Geometry: Parabola, Ellipse and Hyperbola Part II

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.

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: Parabola, Ellipse and Hyperbola Series

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

Analytic Geometry: Parabola, Ellipse and Hyperbola MCQs

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

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

Continue Practice Exam Test Questions Part II of the Series

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)

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

• A. 4p
• B. 2p
• C. P
• D. -4p

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

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

• A. 12
• B. -3
• C. 3
• D. -12

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

• A. x = 8
• B. x = 4
• C. x = -8
• D. x = -4

56. The curve y = –x² + x + 1 opens:

• A. Upward
• B. To the left
• C. To the right
• D. Downward

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

• A. To the right
• B. To the left
• C. Upward
• D. Downward

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

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

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

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

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

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

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

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

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

• A. 0.725
• B. 0.256
• C. 0.689
• D. 0.866

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

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)

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

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

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

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

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

• A. 2
• B. 3
• C. 4
• D. 8

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

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

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

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

78. The chords of the ellipse 64^2 + 25y^2 = 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

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

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

• A. 2
• B. -2
• C. 3
• D. -3

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

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

• A. 0
• B. 2
• C. -2
• D. 1

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

• A. Hyperbola
• B. Parabola
• C. Ellipse
• D. Circle

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

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

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

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

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

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

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

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

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

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

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)

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

• A. 9.84
• B. 10.14
• C. 6.13
• D. 12.14

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

• A. x = √3 x
• B. y = x
• C. 3y = √3 x
• D. y =√3 x

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)

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.

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

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

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