91Ó°ÊÓ

\(9-16=(\) a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic. $$ r=\frac{12}{3-10 \cos \theta} $$

Find \(d y / d x\) and \(d^{2} y / d x^{2} .\) For which values of \(t\) is the curve concave upward? $$x=t^{3}+1, \quad y=t^{2}-t$$

Sketch the curve and find the area that it encloses. $$r=1-\sin \theta$$

\(9-16=(\) a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic. $$ r=\frac{2}{3+3 \sin \theta} $$

Sketch the curve and find the area that it encloses. $$r=3+2 \cos \theta$$

\(9-14=\) (a) Eliminate the parameter to find 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. \(x=\sin t, \quad y=\csc t, \quad 0 < t < \pi / 2\)

Find \(d y / d x\) and \(d^{2} y / d x^{2} .\) For which values of \(t\) is the curve concave upward? $$x=e^{t}, \quad y=t e^{-t}$$

Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. $$2

Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. $$-1 \leqslant r \leqslant 1, \quad \pi / 4 \leqslant \theta \leqslant 3 \pi / 4$$

\(9-14=\) (a) Eliminate the parameter to find 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. $$x=e^{t}-1, \quad y=e^{2 t}$$