91Ó°ÊÓ

Identify the curve by finding a Cartesian equation for the curve. \(r=5 \cos \theta\)

\(17-20\) Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. $$ x=t^{3}-3 t, \quad y=t^{2}-3 $$

(a) Eliminate the parameter to ind a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. $$ x=\tan ^{2} \theta, \quad y=\sec \theta, \quad-\pi / 2<\theta<\pi / 2 $$

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. $$ x=t^{3}-3 t, \quad y=t^{3}-3 t^{2} $$

Graph the conic \(r=4 /(5+6 \cos \theta)\) and its directrix. Also graph the conic obtained by rotating this curve about the origin through an angle \(\pi / 3\).

Find the area of the region enclosed by one loop of the curve. $$ r^{2}=4 \cos 2 \theta $$

\(19-24\) Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph. $$ \frac{y^{2}}{25}-\frac{x^{2}}{9}=1 $$

Describe the motion of a particle with position \((x, y)\) as \(t\) varies in the given interval. $$ x=5+2 \cos \pi t, \quad y=3+2 \sin \pi t, \quad 1 \leqslant t \leqslant 2 $$

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. $$ x=\cos \theta, \quad y=\cos 3 \theta $$

Identify the curve by finding a Cartesian equation for the curve. \(r^{2} \cos 2 \theta=1\)