91Ó°ÊÓ

Plot the point with the rectangular coordinates. Then find the polar coordinates of the point taking \(r>0\) and \(0 \leq \theta<2 \pi\). \((5,-12)\)

(a) find the eccentricity and an equation of the directrix of the conic, (b) identify the conic, and (c) sketch the curve. \(r=\frac{1}{3-2 \cos \theta}\)

Find the points on the curve at which the tangent line is either horizontal or vertical. Sketch the curve. $$ x=1+3 \cos t, \quad y=2-2 \sin t $$

Find the foci and vertices of the ellipse, and sketch its graph. $$ \frac{x^{2}}{4}+\frac{y^{2}}{25}=1 $$

(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. \(x=\cos \theta, \quad y=\cos 2 \theta\)

(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. \(x=\sec \theta, \quad y=\cos \theta\)

Find the foci and vertices of the ellipse, and sketch its graph. $$ \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 $$

Plot the point with the rectangular coordinates. Then find the polar coordinates of the point taking \(r>0\) and \(0 \leq \theta<2 \pi\). \((3,-1)\)

(a) find the eccentricity and an equation of the directrix of the conic, (b) identify the conic, and (c) sketch the curve. \(r=\frac{12}{3+\cos \theta}\)

(a) find the eccentricity and an equation of the directrix of the conic, (b) identify the conic, and (c) sketch the curve. \(r=\frac{1}{1-\sin \theta}\)