MAT141 Review Chapter 7Blitzer1 Find the conic section represented by the equation100 4 812 2x y  .a. Ellipseb. Hyperbolac. Parabolad. Circle2. The directrix of 212y x=- isa. x = 3.b. y = 3.c. x = -3.d. y = -3.3. The foci of 2 225( 1) 36( 2) 900x y- + + = area.( 1, 2 11)- �.b.( 3, 1 11)- - �.c.(1 11, 2)� -.d.(4, 1 11)- �.4. Find the equations that represent ellipses. (i) 2 7 3 9 232 2x y x y    0 (ii) 25 4 4 14 242 2x y x y    0 (iii) 9 3 4 15 152 2x y x y    0a. ii onlyb. i, ii, and iiic. i and ii onlyd. i only5. What is true of212 39 0y y x+ - + =?a. The parabola opens down with a vertex at (6,-3).b. The parabola opens left with a vertex at (-3,6).c. The parabola opens down with a vertex at (-6,-3).d. The parabola opens right with a vertex at (3,-6).6. 2 214 36x y- = has asymptotes ata.3y x=�.b.13y x=�.c.2y x=�.d.6y x=�.1MAT141 Review Chapter 7Blitzer7. Find the graph of the equation16 9 1442 2x y .a.xy  b. xy c.xy  d. xy 8. Find an equation that represents the graph.xy–10 10–1010a.4 36 144 02 2x y  b.4 36 144 02 2y x  c.36 4 144 02 2x y  d.36 4 144 02 2y x  2MAT141 Review Chapter 7Blitzer9. Find the equation of a parabola with focus at (-1, 4) and directrix x = 7.a. 2( 4) 16( 3)x y- =- -b.2( 4) 16( 3)y x- =- -c. 2( 3) 16( 4)y x- =- -d.2( 3) 16( 4)x y- =- -10. 2 2( 3) ( 1)1100 64x y- -- = has vertices ata. (-13,-1), (7,-1).b. (-7,1), (13,1).c. (-7,-1), (13,-1).d. (-6,1), (14,1).11. Find the equation of the parabola with vertex at the origin that passes through the point– ,81 3 b g and opens to the left.a. x y 92b. y x 92c. x y92d. y x9212. Find the equation of the ellipse with foci at (0,7), (0, -7) and y-intercepts at ( ) ( )0, 8 and 0,8-.a.2 2115 64x y+ =b.2 2149 15x y+ =c.2 2164 15x y+ =d.2 2149 64x y+ =13. Find the equation of the parabola with vertex at the origin that passes through the point( )3, 9- and opens downward.a.x y2b.y x2c.y x2d.x y23MAT141 Review Chapter 7Blitzer 14. The arch beneath a bridge is semi-elliptical and a one-way road passes under the arch. The road is 38 feet wide and the height of the arch over the center of the roadway is 9 feet. Two trucks plan to use the road and both are 12 feet wide. Truck 1 is 8 feet high and truck 2 is 7 feet high. Which of the following is true?a. Only Truck 2 can pass under the bridge.b. Only Truck 1 can pass under the bridge.c. Neither truck can pass under the bridge.d. Both trucks can pass under the bridge.15. Identify the type of graph and find the center:2 29 4 18 16 11 0x y x y+ - + - =.a. ellipse; center (-2,1)b. hyperbola; center(-2,-1)c. hyperbola; center(1,-2)d. ellipse; center(1,-2)16. Describe the translation of the graph of the conic represented by the equationx y4252412 2bgbg.a. The graph of the ellipse has been shifted four units to the right and two units upward from standard position.b. The graph of the ellipse has been shifted four units to the left and two units downward from standard position.c. The graph of the ellipse has been shifted four units to the left and two units upward from standard position.d. The graph of the ellipse has been shifted four units to the right and two units downward from standard position.17. The axis of symmetry of 2( 3) 8( 1)x y- = + isa. y = -1.b. y = 3.c. x = 3.d. x = -1.18. A bridge is built in the shape of a parabolic arch. The arch has a span of 154 feet and a maximum height of 30 feet. Find the height of the arch 20 feet from its center.a. 0.5 ft.b. 8.1 ft.c. 28 ft.d. 342 ft.4MAT141 Review Chapter 7Blitzer19. An ellipse has vertices at 13, 0b g and foci at 5, 0b g. Find the equation of the ellipse in standard form. a. x y2 2169 1441  b. x y2 2144 1691  c. x y2 2169 251  d. x y2 225 1691 20. Find the focus and directrix of the parabola y x= 1122 .a. Focus: – 3 0, b gDirectrix: x 3b. Focus: ( )0, 3- Directrix: y 3c. Focus: 0 3, b gDirectrix: x 3d. Focus: 0 3, b gDirectrix: y 321. Find the equation that represents the graph. a. x y2 236 81 1b. x y2 29 6 1c.2 2181 36x y+ =d.x y2 26 9 15xy MAT141 Review Chapter 7Blitzer22. Find the foci of the hyperbola2 24 9 36x y- =.a. (2,0), (-2,0)b. (0,2), (0,-2)c.( 13, 0),( 13, 0)-d.(0, 13, ), (0, 13,)-23. Find the equations that represent parabolas. (i) 2 5 15 252y x y   0 (ii) 13 5 2 4 252 2x y x y    0 (iii) 10 3 11 142y x y   0a. iii only b. ii and iii only c. i and iii only d. i and ii only24. The line through the foci of an ellipse intersects the ellipse at itsa. vertices.b. minor axis.c. major axis.d. endpoints.25. The asymptotes of a hyperbolaa. cross the vertices of the hyperbola.b. intersect at the center of the hyperbola.c. always have the equation y x=�.d. only occur when a hyperbola is centered at the origin.6MAT141 Review Chapter 7BlitzerKey for Chapter 7 Review1.b 16. a2. a 17. c3.c 18. c4. a 19. a5. d 20. b6. a 21. a7. d 22. c8. c 23. c9. b 24. a10. b 25. b11. a12. a13. b14. d15.