project 7 pre calc

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. In Exercises 1-3, graph the conic and identify any vertices and foci. (-10. 3) 1. yz - 8x = 0 2. yz - 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 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 = +2x. 7. Use a graphing utility to graph the conic x2 - = 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 + bry + ) - 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 = 1 - 6 11. x = V/ + 2 12. x = 2 + 3 cos # - 1 y = 2 sin a 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 + 432 - 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 + y? - 12y = 0 to polar form. 19. Convert the polar equation / = 2 sin @ 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 0 22. = = 2 + 3 sin 0 23. Find a polar equation of an ellipse with its focus at the pole, an eccentricity of e = 7, and directrix at y = 4. 24. Find a polar equation of a hyperbola with its focus at the pole, an eccentricity of e = i, and directrix at y = 2. 25. For the polar equation r = 8 cos 30, find the maximum value of | | and any zeros of r. Verify your answers numerically