91Ó°ÊÓ

(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. \(x=2 \sin \theta, \quad y=2 \cos \theta ; \quad 0 \leq \theta \leq 2 \pi\)

(a) find the eccentricity and an equation of the directrix of the conic, (b) identify the conic, and (c) sketch the curve. \(r=\frac{8}{6+2 \sin \theta}\)

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

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

(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. \(x=\cos 2 \theta, \quad y=3 \sin \theta ; \quad 0 \leq \theta \leq 2 \pi\)

(a) find the eccentricity and an equation of the directrix of the conic, (b) identify the conic, and (c) sketch the curve. \(r=\frac{8}{6-2 \sin \theta}\)

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

Plot the point with the rectangular coordinates. Then find the polar coordinates of the point taking \(r>0\) and \(0 \leq \theta<2 \pi\). \((1,-1)\)

Plot the point with the rectangular coordinates. Then find the polar coordinates of the point taking \(r>0\) and \(0 \leq \theta<2 \pi\). \((0,5)\)

(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. \(x=2 \sin \theta, \quad y=3 \cos \theta ; \quad 0 \leq \theta \leq 2 \pi\)