Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/213

8. The curve	${\begin{cases}x=a(\cos t+t\sin t),\\y=a(\sin t-t\cos t).\end{cases}}$	Ans.	${\begin{cases}\alpha =a\cos t,\\\beta =a\sin t.\end{cases}}$
9. The curve	${\begin{cases}x=3t,\\y=t^{2}-6.\end{cases}}$		${\begin{cases}\alpha =-{\frac {4}{3}}t^{3},\\\beta =3t^{2}-{\frac {3}{2}}.\end{cases}}$
10. The curve	${\begin{cases}x=6-t^{2}\\y=2t.\end{cases}}$		${\begin{cases}\alpha =4-3t^{2},\beta =-2t^{3}.\end{cases}}$
11. The curve	${\begin{cases}x=2t,\\y=t^{2}-2.\end{cases}}$		${\begin{cases}\alpha =-2t^{3},\\\beta =3t^{2}.\end{cases}}$
12. The curve	${\begin{cases}x=4t,\\y=3+t^{2}.\end{cases}}$		${\begin{cases}\alpha =-t^{3},\\\beta =11+3t^{2}.\end{cases}}$
13. The curve	${\begin{cases}x=9-t^{2},\\y=2t.\end{cases}}$		${\begin{cases}\alpha =7-3t^{2},\beta =-2t^{3}.\end{cases}}$
14. The curve	${\begin{cases}x=2t,\\y={\frac {1}{3}}t^{3}.\end{cases}}$		${\begin{cases}\alpha ={\frac {4t-t^{5}}{4}}.\\\beta ={\frac {12+5t^{4}}{6t}}.\end{cases}}$
15. The curve	${\begin{cases}x={\frac {1}{3}}t^{3},\\y=t^{2}.\end{cases}}$		${\begin{cases}\alpha ={\frac {4t^{3}+12t}{3}}\\\beta =-{\frac {2t^{2}+t^{4}}{2}}.\end{cases}}$
16. The curve	${\begin{cases}x=2t,\\y={\frac {3}{t}}.\end{cases}}$		${\begin{cases}\alpha ={\frac {12t^{4}+9}{4t^{3}}}\\\beta ={\frac {27+4t^{4}}{6t}}.\end{cases}}$

17. $x=4-t^{2},\ y=2t.$	22. $x=t,\ y=t^{3}.$
18. $x=2t,\ y=16-t^{2}.$	23. $x=\sin t,\ y=3\cos t.$
19. $x=t,\ y=\sin t.$	24. $x=1-\cos t,\ y=t-\sin t.$
20. $x={\frac {4}{t}},\ y=3t.$	25. $x=\cos ^{4}t,\ y=\sin ^{4}t.$
21. $x=t^{2},\ y={\frac {1}{6}}t^{3}.$	26. $x=a\sec t,\ y=b\tan t.$

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