Take this test as you would take a test in class. After you are finished, check your 11 (-2, 3) work against the answers given in the back of the book. (-6, 10) In Exercises 1-3, graph the conic and identify any vertices and foci. (-10.3)/ 1. y2 - 8x = 0 2. 32 - 4x + 4 = 0 3. x2 - 4)2 - 4x = 0 -19 4. Find the standard form of the equation of the parabola with focus (8, -2) and (-6, -4) directrix x = 4, and sketch the parabola. -5 5. Find the standard form of the equation of the ellipse shown at the right. Figure for 5 6. Find the standard form of the equation of the hyperbola with vertices (0, +3) and asymptotes y = +5x. 7. Use a graphing utility to graph the conic x - = 1. Describe your viewing window. 8. (a) Determine the number of degrees the axis must be rotated to eliminate the xy-term of the conic x- + 6xy + y2 - 6 = 0. (b) Graph the conic in part (a) and use a graphing utility to confirm your result. [x2 + 212 - 4x + 6y - 5 =0 9. Solve the system of equations at the right algebraically by the method of substitution. xty + 5=0 Then verify your results by using a graphing utility. System for 9 In Exercises 10-12, sketch the curve represented by the parametric equations. Then eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. 10. x = 12 - 6 11. x = V/' + 2 12. x = 2 + 3 cos 0 y = 2 sin e In Exercises 13-15, find two different sets of parametric equations for the given rec- tangular equation. (There are many correct answers.) 13. y = x2 + 10 14. x + y = 4 15. x2 + 4y2 - 16 = 0 16. Convert the polar coordinate (-14, to rectangular form. 17. Convert the rectangular coordinate (2, -2) to polar form and find two additional polar representations of this point. (There are many correct answers.) 18. Convert the rectangular equation x2 + y2 - 12y = 0 to polar form. 19. Convert the polar equation / = 2 sin 0 to rectangular form. In Exercises 20-22, identify the conic represented by the polar equation algebraically. Then use a graphing utility to graph the polar equation. 20. r = 2 + 3 sin 0 21. r= 1 - cos e 22. r = 7 2 + 3 sin 0 23. Find a polar equation of an ellipse with its focus at the pole, an eccentricity of e = 4, and directrix at y = 4. 24. Find a polar equation of a hyperbola with its focus at the pole, an eccentricity of e = 3, and directrix at y = 2. 25. For the polar equation r = 8 cos 30, find the maximum value of |r| and any zeros of r. Verify your answers numerically