Name: Date: 1. Match the equation with its graph. Page 1

Transcription

1 Name: Date: 1. Match the equation with its graph. y 6x A) C) Page 1

2 D) E) Page

3 . Match the equation with its graph. ( x3) ( y3) A) C) Page 3

4 D) E) Page 4

5 3. Match the equation with its graph. ( x ) y 1 4 A) 1 C) Page 5

6 D) E) none of the above. 4. Find the focus of the parabola given by x y A) 5, 1, 4 5, C) D) E) 9, 4 1, Page 6

7 5. Find the vertex, focus, and directrix of the parabola and sketch its graph. y 6y4x50 A) vertex: (1, 3); focus: (0, 3); directrix x = vertex: (1, 3); focus: (0, 3); directrix x = C) vertex: ( 1,3); focus: (, 3); directrix x = 0 Page 7

8 D) vertex: ( 1,3); focus: (, 3); directrix x = 0 E) vertex: (1, 3); focus: (, 3); directrix x = 0 6. Find an equation of the parabola with vertex (0,5) and directrix y = 9. A) y 8( x5) C) D) E) x y x x 56( y5) 56( x5) 56( y5) 8( y5) Page 8

9 7. Find the center, foci, vertices, and eccentricity of the ellipse. ( x 3) ( y+ 3) A) center: (3, 3); vertices: (, 3), (8, 3); foci: (3, 7), (7,1); eccentricity: center: (3, 3); vertices: (3, 8), (3,); foci: (3, 7), (3,1); eccentricity: C) center: (3, 3); vertices: (, 3), (8, 3); foci: ( 1, 3), (7, 3); eccentricity: D) center: (3, 3); vertices: (, 3), (8, 3); foci: ( 1, 3), (7, 3); eccentricity: E) center: (3, 3); vertices: (, 3), (8, 3); foci: ( 1, 3), (7, 3); eccentricity: Find the vertices of the ellipse given by 16x 9y 18x18 y A) 4,3, 4, 5 4,4, 4, C) 1,1, 1,1 D) 0,1, 0,1 E) 4,5, 4, 3 9. Find the center, foci, and vertices of the hyperbola. ( x1) ( y) A) center: (1, ); vertices: (1, 3), (1, 1); foci: 1, 10, 1, 10. center: (1, ); vertices: (, ), (4, ); foci: 1, 10, 1, 10. C) center: (1, ); vertices: (1, 3), (1, 1); foci: 1 10,, 1 10,. D) center: (1, ); vertices: (, ), (4, ); foci: 1 10,, 1 10,. E) center: (1, ); vertices: (, ), ( 4, ); foci: 1, 10, 1, 10. Page 9

10 10. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 10x 8y 7xy6 0 A) parabola circle C) ellipse D) hyperbola 11. Suppose a cable of a suspension bridge is suspended (in the shape of a parabola) between two towers that are 180 meters apart and 30 meters above the roadway as shown in the figure given below. The cable touches the roadway midway between the towers. Find an equation for the parabolic shape of cable. A) C) D) E) 1 y x 5 1 y x 70 1 y x 135 y 70x y 135x Page 10

11 1. Write the corresponding rectangular equation for the curve represented by the parametric equation x 5t7, y t 9 by eliminating the parameter. A) x y590 x5y30 C) x5y590 D) x5y30 E) x y590 Page 11

12 13. Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter. x 1 6cos y 3 3sin A) 4 y ( x 1) 1 3 y x x 3, 0 C) y x 3 1 Page 1

13 D) x y E) none of the above. 14. Find a set of parametric equations for the rectangular equation y x 1 that satisfies the condition t 0 at the point (1,1). A) x t, y t1 x t1, y t + 1 C) x t1, y t + 1 D) E) x t y t t, x t y t t 1, Find a set of parametric equations for the rectangular equation condition t 5 at the point (5,50). A) x t, y 10t x t5, y 10t50 C) x t, y t D) E) x t, y t xt y t t 5, 0 50 y x that satisfies the 16. Identify any points at which the cycloid x sin, y 1 cos is not smooth. 1 A) not smooth when ( n 1) smooth everywhere C) not smooth when n D) not smooth when ( n +1) E) not smooth when ( n) Page 13

14 17. Find dy dx. x 11 t y 4 t A) C) D) E) dy 11t dx dy 4t dx dy 11t dx 10 dy 11 11t dx 1 dy 11 4t dx Find the second derivative d y dx your answer to two decimal places, if necessary. A) C) D) E) 1.50 of the parametric equations x 6, t y 4t. Round 19. Find an equation of the tangent line at a point 0,0 on the curve A) yx 0 yx 0 C) yx 0 D) yx 0 E) yx 0 x t 4, y t t. Page 14

15 0. Find all points (if any) of horizontal and vertical tangency to the curve x 7cos, y 3 sin. A) horizontal tangents: 7, 4, 7, 4, vertical tangents: 9, 3, 5, 3 horizontal tangent: 9, 3, vertical tangent: 7, C) horizontal tangent: 7,, vertical tangent: 9, 3 D) horizontal tangents: 7,, 7, 4, vertical tangents: 9, 3, 5, 3 E) horizontal tangents: 9, 3, 5, 3, vertical tangents: 7,, 7, 4 1. Find the arc length of the curve answer to three decimal places. A) C) D) E) , 3 on the interval 1 t 4 x t y t. Round your. Find the arc length of the curve on the given interval. xt, y 8 t, 0t 4 A) 16 ln ln 16 ln ln C) 4 ln D) 4 ln ln E) 4 ln ln 3. Find the area of the surface generated by revolving the curve x, t y 5t about the x- axis on the interval 0t 3. A) C) 5 9 D) 45 9 E) 9 9 Page 15

16 Find the area of the surface generated by revolving the curve x t, y t 9 about 3 the y-axis on the interval t 3. Round your answer to two decimal places. A) C) D) E) Find the corresponding rectangular coordinates for the point r, 4,.31. Round your answer to three decimal places. xy, 1.347,.334 A) xy,.560,1.478 C) xy, 1.347,1.478 D) xy, 1.347, E) xy, 5.10, Find two sets of polar coordinates for the point 0, 11 A) C) D) E) 3 11,, 11, ,, 11, 3 11,, 11, 3 11,, 11, 4 4 3,,, for 0. Page 16

17 7. Match the graph with its polar equation. A) r sin r 4cos( ) C) r 3(1 cos ) D) r sec E) r 3(1 sin ) 8. Convert the rectangular equation A) r 10 r 100 C) r 0 D) r 40 E) r 5 x y 100 to polar form. 9. Convert the polar equation to rectangular form. r 8 A) x 8 x ( y8) 64 C) x y 64 D) 9x y8 0 E) y 8 Page 17

18 30. Find the points of intersection of the graphs of the equations. r.4 r.4.4,5.76 A).4,5.76 C).4,.4 D).4,.4 E).4, Find the length of the curve over the given interval. r 77sin, 0 A) 4 56 C) 8 D) 14 E) 7 Page 18

19 Answer Key 1. A. D 3. E 4. B 5. A 6. D 7. E 8. E 9. D 10. D 11. B 1. C 13. E 14. B 15. D 16. E 17. C 18. B 19. D 0. D 1. A. B 3. D 4. E 5. C 6. C 7. B 8. A 9. C 30. E 31. B Page 19