91Ó°ÊÓ

(a) find the eccentricity and an equation of the directrix of the conic, (b) identify the conic, and (c) sketch the curve. \(r=\frac{5}{2+2 \cos \theta}\)

Sketch the curve, and find the area of the region enclosed by it. $$ r=3 \sin \theta $$

Find the points on the curve at which the tangent line is either horizontal or vertical. Sketch the curve. $$ x=t^{2}-4, \quad y=t^{3}-3 t $$

Find the vertex, focus, and directrix of the parabola with the given equation, and sketch the parabola. $$ 5 y^{2}=12 x $$

(a) find the eccentricity and an equation of the directrix of the conic, (b) identify the conic, and (c) sketch the curve. \(r=\frac{5}{2-2 \sin \theta}\)

(a) find a rectangular equation whose graph contains the curve \(C\) with the given parametric equations, and (b) sketch the curve \(\mathrm{C}\) and indicate its orientation. \(x=\sin \theta+3, \quad y=3 \cos \theta+1 ; \quad 0 \leq \theta \leq 2 \pi\)

Plot the point with the rectangular coordinates. Then find the polar coordinates of the point taking \(r>0\) and \(0 \leq \theta<2 \pi\). \((2 \sqrt{3},-2)\)

Sketch the curve, and find the area of the region enclosed by it. $$ r=2(1-\cos \theta) $$

Find the vertex, focus, and directrix of the parabola with the given equation, and sketch the parabola. $$ y^{2}=-40 x $$

Find the points on the curve at which the tangent line is either horizontal or vertical. Sketch the curve. $$ x=t^{3}-3 t, \quad y=t^{2} $$