91Ó°ÊÓ

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ \frac{y^{2}}{9}-\frac{x^{2}}{25}=1 $$

For the following exercises, graph the parabola, labeling the focus and the directrix $$ y=\frac{1}{36} x^{2} $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 $$

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. $$ r=\frac{10}{5-4 \sin \theta} $$

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. $$ r=\frac{3}{1+2 \cos \theta} $$

For the following exercises, find the foci for the given ellipses. $$ 4 x^{2}+9 y^{2}=1 $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ 4 x^{2}+9 y^{2}=1 $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(81 x^{2}-9 y^{2}=1\)

For the following exercises, rotate through the given angle based on the given equation. Give the new equation and graph the original and rotated equation. $$\frac{y^{2}}{16}+\frac{x^{2}}{9}=1, \theta=45^{\circ}$$

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ 81 x^{2}-9 y^{2}=1 $$