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

 {| style="width: 100%;" 4t, \\ y = 3 + t^2. \end{cases}$$
 * 8. The curve
 * $$\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 = -2 t^3, \\ \beta = 3t^2. \end{cases}$$
 * 12. The curve
 * $$\begin{cases} x =
 * 11. The curve
 * $$\begin{cases} x = 2t, \\ y = t^2 - 2. \end{cases}$$
 * $$\begin{cases} \alpha = -2 t^3, \\ \beta = 3t^2. \end{cases}$$
 * 12. The curve
 * $$\begin{cases} x =
 * 12. The curve
 * $$\begin{cases} x =
 * $$\begin{cases} \alpha = -t^3, \\ \beta = 11 + 3t^2. \end{cases}$$
 * 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
 * $$\begin{cases} x = 2t, \\ y = \frac{3}{t}. \end{cases}$$
 * $$\begin{cases} \alpha = \frac{12t^4 + 9}{4t^3} \\ \beta = \frac{27 + 4t^4}{6t}. \end{cases}$$
 * }
 * $$\begin{cases} x = \frac{1}{3} t^3, \\ y = t^2. \end{cases}$$
 * $$\begin{cases} \alpha = \frac{4t^3 + 12t}{3} \\ \beta = -\frac{2t^2 + t^4}{2}. \end{cases}$$
 * 16. The curve
 * $$\begin{cases} x = 2t, \\ y = \frac{3}{t}. \end{cases}$$
 * $$\begin{cases} \alpha = \frac{12t^4 + 9}{4t^3} \\ \beta = \frac{27 + 4t^4}{6t}. \end{cases}$$
 * }
 * $$\begin{cases} \alpha = \frac{12t^4 + 9}{4t^3} \\ \beta = \frac{27 + 4t^4}{6t}. \end{cases}$$
 * }
 * }