91Ó°ÊÓ

For the following exercises, rewrite the given equation in standard form, and then determine the vertex \((V),\) focus \((F),\) and directrix \((d)\) of the parabola. $$ x^{2}+4 x+8 y-4=0 $$

For the following exercises, convert the polar equation of a conic section to a rectangular equation. $$ r=\frac{6 \csc \theta}{3+2 \csc \theta} $$

For the following exercises, find the equations of the asymptotes for each hyperbola. $$ 16 y^{2}+96 y-4 x^{2}+16 x+112=0 $$

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ \frac{x^{2}}{49}-\frac{y^{2}}{16}=1 $$

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. $$ r=\frac{5}{2+\cos \theta} $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(\frac{x^{2}}{49}-\frac{y^{2}}{16}=1\)

For the following exercises, find the foci for the given ellipses. $$ 10 x^{2}+y^{2}+200 x=0 $$

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. $$ r=\frac{5}{2+\cos \theta} $$

For the following exercises, graph the parabola, labeling the focus and the directrix. $$ x=\frac{1}{8} y^{2} $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(\frac{x^{2}}{64}-\frac{y^{2}}{4}=1\)