Chapter 8

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, find the foci for the given ellipses. $$ \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 $$

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. $$\frac{x^{2}}{4}+\frac{y^{2}}{1}=1, \theta=45^{\circ}$$

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

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, graph the parabola, labeling the focus and the directrix $$ y=-9 x^{2} $$

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

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

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

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. $$\frac{y^{2}}{16}+\frac{x^{2}}{9}=1, \theta=45^{\circ}$$

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

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. $$ r=\frac{8}{4-5 \cos \theta} $$

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. $$ r=\frac{8}{4-5 \cos \theta} $$

For the following exercises, graph the parabola, labeling the focus and the directrix $$ (y-2)^{2}=-\frac{4}{3}(x+2) $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ 81 x^{2}+49 y^{2}=1 $$

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ \frac{(y+5)^{2}}{9}-\frac{(x-4)^{2}}{25}=1 $$

For the following exercises, find the foci for the given ellipses. $$ 81 x^{2}+49 y^{2}=1 $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(\frac{(y+5)^{2}}{9}-\frac{(x-4)^{2}}{25}=1\)

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. $$ r=\frac{3}{4-4 \cos \theta} $$

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. $$ r=\frac{3}{4-4 \cos \theta} $$

For the following exercises, graph the parabola, labeling the focus and the directrix $$ -5(x+5)^{2}=4(y+5) $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ \frac{(x-2)^{2}}{64}+\frac{(y-4)^{2}}{16}=1 $$

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ \frac{(x-2)^{2}}{8}-\frac{(y+3)^{2}}{27}=1 $$

For the following exercises, find the foci for the given ellipses. $$ \frac{(x-2)^{2}}{64}+\frac{(y-4)^{2}}{16}=1 $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(\frac{(x-2)^{2}}{8}-\frac{(y+3)^{2}}{27}=1\)

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. $$ r=\frac{2}{1-\sin \theta} $$

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. $$ r=\frac{2}{1-\sin \theta} $$

For the following exercises, graph the parabola, labeling the focus and the directrix $$ -6(y+5)^{2}=4(x-4) $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ \frac{(x+3)^{2}}{9}+\frac{(y-3)^{2}}{9}=1 $$

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ \frac{(y-3)^{2}}{9}-\frac{(x-3)^{2}}{9}=1 $$

For the following exercises, find the foci for the given ellipses. $$ \frac{(x+3)^{2}}{9}+\frac{(y-3)^{2}}{9}=1 $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(\frac{(y-3)^{2}}{9}-\frac{(x-3)^{2}}{9}=1\)

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. $$ r=\frac{6}{3+2 \sin \theta} $$

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. $$ r=\frac{6}{3+2 \sin \theta} $$

For the following exercises, graph the parabola, labeling the focus and the directrix $$ y^{2}-6 y-8 x+1=0 $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ \frac{x^{2}}{2}+\frac{(y+1)^{2}}{5}=1 $$

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ -4 x^{2}-8 x+16 y^{2}-32 y-52=0 $$

For the following exercises, find the foci for the given ellipses. $$ \frac{x^{2}}{2}+\frac{(y+1)^{2}}{5}=1 $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(-4 x^{2}-8 x+16 y^{2}-32 y-52=0\)

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. $$ r(1+\cos \theta)=5 $$

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. $$ r(1+\cos \theta)=5 $$

For the following exercises, graph the parabola, labeling the focus and the directrix $$ x^{2}+8 x+4 y+20=0 $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ 4 x^{2}-8 x+16 y^{2}-32 y-44=0 $$

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. $$ x^{2}-8 x-25 y^{2}-100 y-109=0 $$

For the following exercises, find the foci for the given ellipses. $$ 4 x^{2}-8 x+16 y^{2}-32 y-44=0 $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(x^{2}-8 x-25 y^{2}-100 y-109=0\)

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. $$ r(3-4 \sin \theta)=9 $$

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. $$ r(3-4 \sin \theta)=9 $$

For the following exercises, graph the parabola, labeling the focus and the directrix. $$ 3 x^{2}+30 x-4 y+95=0 $$