91Ó°ÊÓ

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, rotate through the given angle based on the given equation. Give the new equation and graph the original and rotated equation. \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1, \theta=30^{\circ}\)

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. \(r=\frac{6}{3+2 \quad \sin \theta}\)

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, 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, graph the parabola, labeling the focus and the directrix. \(x^{2}+8 x+4 y+20=0\)

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

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

For the following exercises, graph the given ellipses, noting center, vertices, and foci. \(x^{2}-8 x+25 y^{2}-100 y+91=0\)

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. \(-x^{2}+8 x+4 y^{2}-40 y+88=0\)