MCQs in Geometry Part IV

This is the Multiple Choice Questions Part 4 of the Series in Geometry topic 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 Lines and Planes | MCQs in lane figures | MCQs in Application of Cavalier's, Pappus and Prismodial Theorems | MCQs in Coordinate in Space | MCQs in Quadratic Surfaces | MCQs in Mensuration | MCQs in Plane Geometry | MCQs in Solid Geometry | MCQs in Spherical Geometry | MCQs in Analytical Geometry

Online Questions and Answers in Geometry Series

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

Geometry MCQs

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

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

PART 3: MCQs from Number 101 – 150                        Answer key: PART III

PART 4: MCQs from Number 151 – 200                        Answer key: PART IV

Continue Practice Exam Test Questions Part IV of the Series

Choose the letter of the best answer in each questions.

151. What is the length of the length of the latus rectum of the curve x^2 = 20y?

• A. sqrt(20)
• B. 20
• C. 5
• D. sqrt(5)

152. Find the location of the focus of the parabola y^2 + 4x – 4y -8 = 0.

• A. (2.5, -2)
• B. (3, 1)
• C. (2, 2)
• D. (-2.5, 2)

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

• A. 7x + 4 = 0
• B. 4x + 7 = 0
• C. 4x – 7 = 0
• D. x – 2 = 0

154. A parabola has its focus at (7, -4) and directrix y = 2. Find the equation.

• A. x^2 + 12y – 14x + 61 = 0
• B. x^2 - 14y + 12x + 61 = 0
• C. x^2 – 12x + 14y + 61 = 0
• D. None of the above

155. A parabola has its axis parallel to the x-axis, vertex at (-1, 7) and one end of the latus rectum at (-15/4, 3/2). Find its equation.

• A. y^2 – 11y + 11x – 60 = 0
• B. y^2 – 11y + 14x – 60 = 0
• C. y^2 – 14y + 11x + 60 = 0
• D. None of the above

156. Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x – 6y + 25 = 0.

• A. 2, 8
• B. 4, 16
• C. 16, 64
• D. 1, 4

157. Given a parabola (y – 2)^2 = -8(x – 1). What is the equation of its directrix?

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

158. The general equation of a conic section is given by the following equation: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0. A curve maybe identified as an ellipse by which of the following conditions?

• A. B^2 – 4AC < 0
• B. B^2 – 4AC = 0
• C. B^2 – 4AC > 0
• D. B^2 – 4AC = 1

159. What is the area enclosed by the curve 9x^2 + 25y^2 – 225 = 0?

• A. 47.1
• B. 50.2
• C. 63.8
• D. 72.3

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

• A. 2x^2 – 4y^2 = 5
• B. 4x^2 + 3y^2 = 12
• C. 2x^2 + 5y^3 = 3
• D. x^2 + 2y^2 = 4

161. The lengths of the major and minor axes of an ellipse are 10m and 8m, respectively. Find the distance between the foci.

• A. 3
• B. 4
• C. 5
• D. 6

162. The equation 25x^2 + 16y^2 – 150x + 128y + 81 = 0 has its center at

• A. (3, -4)
• B. (3, 4)
• C. (4, -3)
• D. (3, 5)

163. Find the major axis of the ellipse x^2 + 4y^2 – 2x – 8y + 1 = 0.

• A. 2
• B. 10
• C. 4
• D. 6

164. The length of the latus rectum for the ellipse x^2/64 + y^2/16 = 1 is equal to:

• A. 2
• B. 3
• C. 4
• D. 5

165. An ellipse with an eccentricity of 0.65 and has one of its foci 2 units from the center. The length of the latus rectum is nearest to

• A. 3.5 units
• B. 3.8 units
• C. 4.2 units
• D. 3.2 units

166. An earth satellite has an apogee of 40, 000 km and a perigee of 6, 600 km. Assuming the radius of the earth as 6,400 km, what will be the eccentricity of the elliptical path describes by the satellite with the center of the earth at one of the foci?

• A. 0.46
• B. 0.49
• C. 0.52
• D. 0.56

167. 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. 93,000,000 miles
• B. 91,450,000 miles
• C. 94,335,000 miles
• D. 94,550,000 miles

168. The earth’s orbit is an ellipse with the sun at one of the foci. If the farthest distance of the sun from the earth is 105.50 million km and the nearest distance of the sun from the earth is 78.25 million km, find the eccentricity of the ellipse.

• A. 0.15
• B. 0.25
• C. 0.35
• D. 0.45

169. An ellipse with center at the origin has a length of major axis 20 units. If the distance from the center of ellipse to its focus is 5, what is the equation of its directrix?

• A. x = 18
• B. x = 20
• C. x = 15
• D. x= 16

170. What is the length of the latus rectum of 4x^2 + 9y^2 + 8x – 32 = 0?

• A. 2.5
• B. 2.7
• C. 2.3
• D. 2.9

171. 4x^2 – y^2 + 16 = 0 is the equation of a/an

• A. parabola
• B. hyperbola
• C. circle
• D. ellipse

172. Find the eccentricity of the curve 9x^2 – 4y^2 – 36x + 8y = 4.

• A. 1.80
• B. 1.92
• C. 1.86
• D. 1.76

173. How far from the x-axis is the focus F of the hyperbola x^2 – 2y^2 + 4x + 4y + 4 = 0?

• A. 4.5
• B. 3.4
• C. 2.7
• D. 2.1

174. The semi-transverse axis of the hyperbola x^2/9 – y^2/4 = 1 is

• A. 2
• B. 3
• C. 4
• D. 5

175. 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

176. Find the equation of the hyperbola whose asymptotes are y = ± 2x and which passes through (5/2, 3).

• A. 4x^2 + y^2 + 16 = 0
• B. 4x^2 + y^2 - 16 = 0
• C. x^2 - 4y^2 - 16 = 0
• D. 4x^2 – y^2 = 16

177. Find the equation of the hyperbola with vertices (-4, 2) and (0, 2) and foci at (-5, 2) and (1, 2).

• A. 5x^2 – 4y^2 + 20x + 16y – 16 = 0
• B. 5x^2 – 4y^2 + 20x - 16y – 16 = 0
• C. 5x^2 – 4y^2 - 20x + 16y + 16 = 0
• D. 5x^2 + 4y^2 - 20x + 16y – 16 = 0

178. Find the distance between P₁ (6, -2, -3) and P₂ (5, 1, 4).

• A. 11
• B. sqrt(11)
• C. 12
• D. sqrt(12)

179. The point of intersection of the planes x + 5y – 2z = 9; 3x – 2y + z = 3 and x + y + z = 2 is at

• A. (2, 1, -1)
• B. (2, 0, -1)
• C. (-1, 1, -1)
• D. (-1, 2, 1)

180. What is the radius of the sphere center at the origin that passes the point 6, 1, 6?

• A. 10
• B. 9
• C. sqrt(101)
• D. 10.5

181. The equation of a sphere with center at (-3, 2, 4) and of radius 6 units is

• A. x^2 + y^2 + z^2 + 6x – 4y – 8z = 36
• B. x^2 + y^2 + z^2 + 6x – 4y – 8z = 7
• C. x^2 + y^2 + z^2 + 6x – 4y + 8z = 6
• D. x^2 + y^2 + z^2 + 6x – 4y + 8z = 36

182. Find the polar equation of the circle if its center is at (4, 0) and the radius is 4.

• A. r – 8 cos θ = 0
• B. r – 6 cos θ = 0
• C. r – 12 cos θ = 0
• D. r – 4 cos θ = 0

183. What are the x and y coordinates of the focus of the conic section described by the following equation? (Angle θ corresponds to a right triangle with adjacent side x, opposite side y and hypotenuse r.) r sin²θ = cos θ

• A. (1/4, 0)
• B. (0,π/2)
• C. (0, 0)
• D. (-1/2, 0)

184. Find the polar equation of the circle of radius 3 units and center at (3, 0).

• A. r = 3 cos θ
• B. r = 3 sin θ
• C. r = 6 cos θ
• D. r = 9 sin θ

185. Given the polar equation r = 5 sin θ. Determine the rectangular coordinates (x, y) of a point in the curve when θ is 30^o.

• A. (2.17, 1.25)
• B. (3.08, 1.5)
• C. (2.51, 4.12)
• D. (6, 3)

186. Find the equation of the circle circumscribing a triangle whose vertices are (0, 0), (0, 5) and (3, 3).

• a. x² + y² – x - 5y = 0
• b. x² + y² - 2x – y = 0
• c. x² + y² -5x -5y + 8 = 0
• d. x² + y² – x - 5y + 6 = 0

187. A parabola having its axis along the x-axis passes through (-3, 6). Compute the length of the latus rectum if the vertex is at the origin.

• a. 4
• b. 8
• c. 6
• d. 12

188. A hut has a parabolic cross-section whose height is 30 m. and whose base is 60 m. wide. If the ceiling 40 m. is to be placed inside the hut, how high will it be above the base?

• a. 16.67 m
• b. 15.48 m
• c. 14.47 m
• d. 19.25 m

189. Find the coordinates of the focus of the parabola x² = 4y – 8.

• a. (0, -3)
• b. (0, 3)
• c. (2, 0)
• d. (0, -2)

190. An ellipse has an eccentricity of 1/3. Compute the distance between directrices if the distance between foci is 4.

• a. 18
• b. 36
• c. 32
• d. 38

191. An ellipse has a length of semi-major axis of 300 m. compute the second eccentricity of the eclipse.

• a. 1.223
• b. 1.222
• c. 1.333
• d. 1.233

192. Compute the circumference of an ellipse whose diameters are 14 and 10 meters.

• a. 28.33 m
• b. 38.22 m
• c. 18.75 m
• d. 23.14 m

193. Find the eccentricity of a hyperbola having distance between foci equal to 18 and the distance between directrices equal to 2.

• a. 2
• b. 3
• c. 2.8
• d. 3.7

194. Find the length of the tangent from point (7, 8) to the circle x² + y² – 9 = 0

• a. 10.2
• b. 14.7
• c. 11.3
• d. 13.6

195. What is the equation of the equation of the directrix of the parabola y² = 16x?

• a. x = 4
• b. y = 4
• c. x = -4
• d. y = -4

196. Find the radius of the circle 2x² + 2y² – 3x + 4y – 1 = 0

• a.  √13/ 4
• b. √30 / 4
• c.  √35 / 4
• d.  √33 / 4

197. Find an equation for the hyperbola with foci at (1, 3) and (9, 3), and eccentricity 2.

• a. x² – 3y² – 30x + 6y + 54 = 0
• b. 3x² – y² – 30x + 6y + 54 = 0
• c. x² – y² – 30 x + 6y + 54 = 0
• d. 3x² – y² – 6x + 30y = 54 = 0

198. Find the equation of the locus of a point which moves so that its distance from (1, -7) is always 5.

• a. x² + y² – 2x + 14y + 25 = 0
• b. x² + y² – 2x – 14y + 25 = 0
• c. x² + y² + 2x + 14y + 25 = 0
• d. x² + y² – 2x + 14y + 25 = 0

199. The difference of the distances of a moving point from (1, 0) and (-1, 0) is 1. Find the equation of its locus.

• a. 4x² - 12y² = 3
• b. 3x² - 4y² = 12
• c. 12x² - 4y² = 3
• d. 4x² - 9y² = 3

200. A circle has its center on the line 2y = 3x and tangent to the x-axis at (4, 0). Find the radius.

• a. 6
• b. 7
• c. 5
• d. 8

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