857 8.8 Parametric Equations, Graphs, and Applications 8.8 Exercises CONCEPT PREVIEWFill in the blank to correctly complete each sentence. 1. For the plane curve defined by x = t2 + 1, y = 2t + 3, for t in 3-4, 44, the ordered pair that corresponds to t = -3 is . 2. For the plane curve defined by x = -3t + 6, y = t2 - 3, for t in 3-5, 54, the ordered pair that corresponds to t = 4 is . 3. For the plane curve defined by x = cos t, y = 2 sin t, for t in 30, 2p4, the ordered pair that corresponds to t = p 3 is . 4. For the plane curve defined by x = 2t, y = t2 + 3, for t in 10, ∞2, the ordered pair that corresponds to t = 16 is . CONCEPT PREVIEW Match the ordered pair from Column II with the pair of parametric equations in Column I on whose graph the point lies. In each case, consider the given value of t. I II 5. x = 3t + 6, y = -2t + 4; t = 2 A. 15, 252 6. x = cos t, y = sint; t = p 4 B. 17, 22 7. x = t, y = t2; t = 5 C. 112, 02 8. x = t2 + 3, y = t2 - 2; t = 2 D. Q 22 2 , 22 2 R For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. See Examples 1 and 2. 9. x = t + 2, y = t2, for t in 3-1, 14 10. x = 2t, y = t + 1, for t in 3-2, 34 11. x = 2t , y = 3t - 4, for t in 30, 44 12. x = t2, y = 2t , for t in 30, 44 13. x = t3 + 1, y = t3 - 1, for t in 1-∞, ∞2 14. x = 2t - 1, y = t2 + 2, for t in 1-∞, ∞2 15. x = 2 sint, y = 2 cos t, for t in 30, 2p4 16. x = 25 sint, y = 23 cos t, for t in 30, 2p4 17. x = 3 tant, y = 2 sec t, for t in A -p 2 , p 2 B 18. x = cot t, y = csc t, for t in 10, p2 19. x = sint, y = csc t, for t in 10, p2 20. x = tant, y = cot t, for t in A0, p 2 B 21. x = t, y = 2t2 + 2, for t in 1-∞, ∞2 22. x = 2t , y = t2 - 1, for t in 30, ∞2
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