Chapter 7

Graph the ellipse. Label the foci and the endpoints of each axis. $$ \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 $$

Sketch a graph of the parabola. $$ x^{2}=y $$

Graph the ellipse. Label the foci and the endpoints of each axis. $$ \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 $$

Sketch a graph of the parabola. $$ x^{2}=-y $$

Graph the ellipse. Label the foci and the endpoints of each axis. $$ \frac{x^{2}}{36}+\frac{y^{2}}{16}=1 $$

Sketch a graph of the parabola. $$ y^{2}=-x $$

Graph the ellipse. Label the foci and the endpoints of each axis. $$ x^{2}+\frac{y^{2}}{4}=1 $$

Sketch a graph of the parabola. $$ y^{2}=x $$

Graph the ellipse. Label the foci and the endpoints of each axis. $$ x^{2}+4 y^{2}=400 $$

Sketch a graph of the parabola. $$ 4 x^{2}=-2 y $$

Graph the ellipse. Label the foci and the endpoints of each axis. $$ 9 x^{2}+5 y^{2}=45 $$

Sketch a graph of the parabola. $$ y^{2}=-3 x $$

Graph the ellipse. Label the foci and the endpoints of each axis. $$ 25 x^{2}+9 y^{2}=225 $$

Sketch a graph of the parabola. $$ y^{2}=-4 x $$

Graph the ellipse. Label the foci and the endpoints of each axis. $$ 5 x^{2}+4 y^{2}=20 $$

Sketch a graph of the parabola. $$ x^{2}=4 y $$

Sketch a graph of the parabola. $$ y^{2}=-\frac{1}{2} x $$

Sketch a graph of the parabola. $$ 8 x=y^{2} $$

Match the equation with its graph \((a-f)\). $$ y^{2}=-8 x $$

Graph the parabola. Label the vertex, focus, and directrix. $$ 16 y=x^{2} $$

Graph the parabola. Label the vertex, focus, and directrix. $$ y=-2 x^{2} $$

Graph the parabola. Label the vertex, focus, and directrix. $$ x=\frac{1}{8} y^{2} $$

Graph the parabola. Label the vertex, focus, and directrix. $$ -y^{2}=6 x $$

Find an equation of the ellipse, centered at the origin, satisfying the conditions. Foci \((0, \pm 2),\) vertices \((0, \pm 4)\)

Graph the parabola. Label the vertex, focus, and directrix. $$ -4 x=y^{2} $$

Find an equation of the ellipse, centered at the origin, satisfying the conditions. Foci \((0, \pm 3),\) vertices \((0, \pm 5)\)

Graph the parabola. Label the vertex, focus, and directrix. $$ \frac{1}{2} y^{2}=3 x $$

Find an equation of the ellipse, centered at the origin, satisfying the conditions. Foci \((\pm 5,0),\) vertices \((\pm 6,0)\)

Graph the parabola. Label the vertex, focus, and directrix. $$ x^{2}=-8 y $$

Find an equation of the ellipse, centered at the origin, satisfying the conditions. Foci \((\pm 4,0),\) vertices \((\pm 6,0)\)

Graph the parabola. Label the vertex, focus, and directrix. $$ x^{2}=-4 y $$

Find an equation of the ellipse, centered at the origin, satisfying the conditions. Horizontal major axis of length \(8,\) minor axis of length 6

Graph the parabola. Label the vertex, focus, and directrix. $$ 2 y^{2}=-8 x $$

Find an equation of the ellipse, centered at the origin, satisfying the conditions. Vertical major axis of length \(12,\) minor axis of length 8

Graph the parabola. Label the vertex, focus, and directrix. $$ -3 x=\frac{1}{4} y^{2} $$

Find an equation of the ellipse, centered at the origin, satisfying the conditions. Bccentricity \(\frac{2}{3},\) horizontal major axis of length 6

Find an equation of the ellipse, centered at the origin, satisfying the conditions. Eccentricity \(\frac{3}{4},\) vertices \((0, \pm 8)\)

Translate the ellipse with the given equation so that it is centered at the given point. Find the new equation and sketch its graph. $$ \frac{x^{2}}{9}+\frac{y^{2}}{2}=1 ;(-3,7) $$

Translate the ellipse with the given equation so that it is centered at the given point. Find the new equation and sketch its graph. $$ \frac{x^{2}}{2}+\frac{y^{2}}{9}=1 ;(-3,-4) $$

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. $$ \text { Focus }\left(0, \frac{3}{4}\right) $$

Translate the ellipse with the given equation so that it is centered at the given point. Find the new equation and sketch its graph. $$ \frac{x^{2}}{15}+\frac{y^{2}}{16}=1 ;(5,-6) $$

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. Directrix \(y=2\)

Sketch a graph of the ellipse. $$ \frac{(x-2)^{2}}{4}+\frac{(y-1)^{2}}{9}=1 $$

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. Directrix \(x=2\)

Sketch a graph of the ellipse. $$ \frac{(x+1)^{2}}{16}+\frac{(y+3)^{2}}{9}=1 $$

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. Focus \((-1,0)\)

Sketch a graph of the ellipse. $$ \frac{(x+1)^{2}}{16}+\frac{(y+2)^{2}}{25}=1 $$

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. Focus \((1,0)\)

Sketch a graph of the ellipse. $$ \frac{(x-4)^{2}}{9}+\frac{y^{2}}{4}=1 $$

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. $$ \text { Focus }\left(0,-\frac{1}{2}\right) $$