Chapter 8

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. $$ -x^{2}+8 x+4 y^{2}-40 y+88=0 $$

For the following exercises, find the foci for the given ellipses. $$ x^{2}-8 x+25 y^{2}-100 y+91=0 $$

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

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. $$ r(3-2 \sin \theta)=6 $$

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. $$ r(3-2 \sin \theta)=6 $$

For the following exercises, graph the parabola, labeling the focus and the directrix. $$ y^{2}-8 x+10 y+9=0 $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ x^{2}+8 x+4 y^{2}-40 y+112=0 $$

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, find the foci for the given ellipses. $$ x^{2}+8 x+4 y^{2}-40 y+112=0 $$

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 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. $$ r(6-4 \cos \theta)=5 $$

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

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

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

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. $$4 x^{2}-3 \sqrt{3} x y+y^{2}-22=0$$

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

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

For the following exercises, graph the parabola, labeling the focus and the directrix. $$ y^{2}+2 y-12 x+61=0 $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ 16 x^{2}+64 x+4 y^{2}-8 y+4=0 $$

For the following exercises, find the foci for the given ellipses. $$ 16 x^{2}+64 x+4 y^{2}-8 y+4=0 $$

Sketch a graph of the hyperbola, labeling vertices and foci. \(-100 x^{2}+1000 x+y^{2}-10 y-2575=0\)

For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=-4 ; e=5\)

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

For the following exercises, graph the parabola, labeling the focus and the directrix. $$ -2 x^{2}+8 x-4 y-24=0 $$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $$ 100 x^{2}+1000 x+y^{2}-10 y+2425=0 $$

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

For the following exercises, find the foci for the given ellipses. $$ 100 x^{2}+1000 x+y^{2}-10 y+2425=0 $$

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

For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(y=2 ; e=2\)

Find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(y=2 ; e=2\)

For the following exercises, find the equation of the parabola given information about its graph. Vertex is (0,0)\(;\) directrix is \(y=4,\) focus is (0,-4) .

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

For the following exercises, given information about the graph of the hyperbola, find its equation. Vertices at (3,0) and (-3,0) and one focus at (5,0)

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

Given information about the graph of the hyperbola, find its equation. Vertices at \((3,0)\) and \((-3,0)\) and one focus at \((5,0)\)

For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(y=-2 ; e=\frac{1}{2}\)

Find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(y=-2 ; e=\frac{1}{2}\)

For the following exercises, find the equation of the parabola given information about its graph. Vertex is (0,0)\(;\) directrix is \(x=4,\) focus is (-4,0) .

For the following exercises, use the given information about the graph of each ellipse to determine its equation. Center at the origin, symmetric with respect to the \(x-\) and \(y\) -axes, focus at \((4,0)\) , and point on graph \((0,3)\)

For the following exercises, given information about the graph of the hyperbola, find its equation. Vertices at (0,6) and (0,-6) and one focus at (0,-8)

Given information about the graph of the hyperbola, find its equation. Vertices at \((0,6)\) and \((0,-6)\) and one focus at \((0,-8) .\)

For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=1 ; e=1\)

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

For the following exercises, find the equation of the parabola given information about its graph. Vertex is (2,2)\(;\) directrix is \(x=2-\sqrt{2},\) focus is \((2+\sqrt{2}, 2)\)

For the following exercises, use the given information about the graph of each ellipse to determine its equation. Center at the origin, symmetric with respect to the \(x-\) and \(y\) -axes, focus at \((0,-2)\) , and point on graph \((5,0)\) .

For the following exercises, given information about the graph of the hyperbola, find its equation. Vertices at (1,1) and (11,1) and one focus at (12,1)