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 y^{2} – 2x + 6y + 3 = 0 is at:

A. (-3, 3)

B. (3, 3)

C. (-3, 3)

D. (-3, -3)

Answer: **Option D**

Solution:

52. The length of the latus rectum of the parabola y^{2} = 4px is:

A. 4p

B. 2p

C. P

D. -4p

Answer: **Option A**

Solution:

53. Given the equation of the parabola: y^{2} – 8x – 4y – 20 = 0. The length of its latus rectum is:

A. 2

B. 4

C. 6

D. 8

Answer: **Option D**

Solution:

54. What is the length of the latus rectum of the curve x^{2} = –12y?

A. 12

B. -3

C. 3

D. -12

Answer: **Option A**

Solution:

55. Find the equation of the directrix of the parabola y^{2} = 6x.

A. x = 8

B. x = 4

C. x = -8

D. x = -4

Answer: **Option D**

Solution:

56. The curve y = –x^{2} + x + 1 opens:

A. Upward

B. To the left

C. To the right

D. Downward

Answer: **Option D**

Solution:

57. The parabola y = –x^{2} + x + 1 opens:

A. To the right

B. To the left

C. Upward

D. Downward

Answer: **Option D**

Solution:

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

A. 4x + 7 = 0

B. x – 2 = 0

C. 4x – 7 = 0

D. 7x + 4 = 0

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. x^{2} + y^{2} – 6x + 3 = 0

B. x^{2} – 6x + 3 = 0

C. 2x^{2} + y^{2} – 6x + 3 = 0

D. y^{2} – 6x + 3 = 0

Answer: **Option D**

Solution:

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

A. y^{2} – 8x + 16y – 32 = 0

B. y^{2} + 8x + 16y – 32 = 0

C. y^{2} + 8x – 16y + 32 = 0

D. x^{2} – 8x + 16y – 32 = 0

Answer: **Option D**

Solution:

61. Find the area bounded by the curves x^{2} + 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

Answer: **Option A**

Solution:

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

A. 11.7

B. 10.7

C. 9.7

D. 4.7

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

Answer: **Option A**

Solution:

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

25x^{2} + 9y^{2} – 300x –144y + 1251 = 0

A. 3.4

B. 3.2

C. 3.6

D. 3.0

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

Answer: **Option B**

Solution:

66. The eccentricity of the ellipse x^{2}/4 + y^{2} / 16 = 1 is:

A. 0.725

B. 0.256

C. 0.689

D. 0.866

Answer: **Option D**

Solution:

67. An ellipse has the equation 16x^{2} + 9y^{2} + 32x – 128 = 0. Its eccentricity is:

A. 0.531

B. 0.66

C. 0.824

D. 0.93

Answer: **Option B**

Solution:

68. The center of the ellipse 4x^{2} + y^{2} – 16x – 6y – 43 = 0 is at:

A. (2, 3)

B. (4, -6)

C. (1, 9)

D. (-2, -5)

Answer: **Option A**

Solution:

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

9x^{2} + 4y^{2} – 72x – 24y – 144 = 0

A. 0.67

B. 1.8

C. 1.5

D. 0.75

Answer: **Option C**

Solution:

70. The area of the ellipse 9x^{2} + 25y^{2} – 36x – 189 = 0 is equal to:

A. 15π sq. units

B. 20π sq. units

C. 25π sq. units

D. 30π sq. units

Answer: **Option A**

Solution:

71. The area of the ellipse is given as A = 3.1416 a b. Find the area of the ellipse 25x^{2} + 16y^{2} – 100x + 32y = 284

A. 86.2 square units

B. 62.8 square units

C. 68.2 square units

D. 82.6 square units

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

Answer: **Option B**

Solution:

73. Given an ellipse x^{2} / 36 + y^{2} / 32 = 1. Determine the distance between foci.

A. 2

B. 3

C. 4

D. 8

Answer: **Option C**

Solution:

74. How far apart are the directrices of the curve 25x^{2} + 9y^{2} – 300x – 144y + 1251 = 0?

A. 12.5

B. 14.2

C. 13.2

D. 15.2

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

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. 9x^{2} + 36y^{2} – 54x + 50y – 116 = 0

B. 4x^{2} + 25y^{2} + 54x – 50y – 122 = 0

C. 9x^{2} + 25y^{2} + 50x + 50y + 109 = 0

D. 9x^{2} + 25y^{2} + 54x + 50y – 119 = 0

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. 4x^{2} + 3y^{2} = 12

B. 2x^{2} – 4y^{2} = 5

C. x^{2} + 2y^{2} = 4

D. 2x^{2} + 5y^{3} = 3

Answer: **Option A**

Solution:

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

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

Answer: **Option B**

Solution:

80. The semi-conjugate axis of the hyperbola (x^{2}/9) – (y^{2}/4) = 1 is:

A. 2

B. -2

C. 3

D. -3

Answer: **Option A**

Solution:

81. What is the equation of the asymptote of the hyperbola (x^{2}/9) – (y^{2}/4) = 1.

A. 2x – 3y = 0

B. 3x – 2y = 0

C. 2x – y = 0

D. 2x + y = 0

Answer: **Option A**

Solution:

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

A. 0

B. 2

C. -2

D. 1

Answer: **Option C**

Solution:

83. The equation x^{2} + Bx + y^{2} + Cy + D = 0 is:

A. Hyperbola

B. Parabola

C. Ellipse

D. Circle

Answer: **Option D**

Solution:

84. The general second degree equation has the form Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F = 0 and describes an ellipse if:

A. B^{2} – 4AC = 0

B. B^{2} – 4AC > 0

C. B^{2} – 4AC = 1

D. B^{2} – 4AC < 0

Answer: **Option D**

Solution:

85. Find the equation of the tangent to the circle x^{2} + y^{2} – 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

Answer: **Option A**

Solution:

86. Find the equation of the tangent to the curve x^{2} + y^{2} + 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

Answer: **Option D**

Solution:

87. Find the equation of the normal to the curve y^{2} + 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

Answer: **Option B**

Solution:

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

A. y = 4x + 1

B. y = 4x – 1

C. y = 2x – 1

D. y = 2x + 1

Answer: **Option B**

Solution:

89. Find the equation of the tangent to the curve x^{2} + y^{2} = 41 through (5, 4).

A. 5x + 4y = 41

B. 4x – 5y = 41

C. 4x + 5y = 41

D. 5x – 4y = 41

Answer: **Option A**

Solution:

90. Find the equation of a line normal to the curve x^{2} = 16y at (4, 1).

A. 2x – y – 9 = 0

B. 2x – y + 9 =

C. 2x + y – 9 = 0

D. 2x + y + 9 = 0

Answer: **Option C**

Solution:

91. What is the equation of the tangent to the curve 9x^{2} + 25y^{2} – 225 = 0 at (0, 3)?

A. y + 3 = 0

B. x + 3 = 0

C. x – 3 = 0

D. y – 3 = 0

Answer: **Option D**

Solution:

92. What is the equation of the normal to the curve x^{2} + y^{2} = 25 at (4, 3)?

A. 3x – 4y = 0

B. 5x + 3y = 0

C. 5x – 3y = 0

D. 3x + 4y = 0

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

Answer: **Option C**

Solution:

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

A. r^{2} = 8

B. r = Ѳ/(cos^{2} Ѳ + 2)

C. r = 8

D. r^{2} = 8/(cos^{2} Ѳ + 2)

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

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

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)

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.

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

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

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**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

**MCQ from Number 51 – 100**Answer key:

**PART 2**

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