91Ó°ÊÓ

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ 64 x^{2}+128 x-9 y^{2}-72 y-656=0 $$

For the following exercises, graph the parabola, labeling the focus and the directrix. $$ x^{2}+4 x+2 y+2=0 $$

For the following exercises, find the foci for the given ellipses. $$ 64 x^{2}+128 x+9 y^{2}-72 y-368=0 $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(16 x^{2}+64 x-4 y^{2}-8 y-4=0\)

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ 64 x^{2}+128 x+9 y^{2}-72 y-368=0 $$

Graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label the vertices and foci. $$ r(6-4 \cos \theta)=5 $$

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ 16 x^{2}+64 x-4 y^{2}-8 y-4=0 $$

For the following exercises, graph the equation relative to the \(x^{\prime} y^{\prime}\) system in which the equation has no \(x^{\prime} y^{\prime}\) 'term. $$4 x^{2}-3 \sqrt{3} x y+y^{2}-22=0$$

For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label the vertices and foci. $$ r(6-4 \cos \theta)=5 $$

Find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=4 ; e=\frac{1}{5}\)