Chapter 7

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

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. $$ \text { Directrix } x=\frac{1}{4} $$

Sketch a graph of the ellipse. $$ x^{2}+\frac{(y-3)^{2}}{4}=1 $$

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

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. Horizontal axis, passing through \((1,-2)\)

Find an equation of the parabola with vertex \((0,0)\) that satisfies the given conditions. Vertical axis, passing through \((-2,3)\)

Find an equation of a parabola that satisfies the given conditions. Focus \((0,-3)\) and directrix \(y=3\)

Find an equation of a parabola that satisfies the given conditions. Focus \((0,2)\) and directrix \(y=-2\)

Sketch a graph of the ellipse. Identify the foci and vertices. $$ \frac{(x-1)^{2}}{9}+\frac{(y-1)^{2}}{25}=1 $$

Find an equation of a parabola that satisfies the given conditions. Focus \((-1,0)\) and directrix \(x=1\)

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

Find an equation of a parabola that satisfies the given conditions. Focus \((3,0)\) and directrix \(x=-3\)

Sketch a graph of the ellipse. Identify the foci and vertices. $$ \frac{(x+4)^{2}}{16}+\frac{(y-2)^{2}}{9}=1 $$

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

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

Sketch a graph of the parabola. $$ (x-2)^{2}=-(y+1) $$

Find an equation of an ellipse that satisfies the given conditions. Center \((2,1),\) focus \((2,3),\) and vertex \((2,4)\)

Sketch a graph of the parabola. $$ (y-1)^{2}=-(x+1) $$

Find an equation of an ellipse that satisfies the given conditions. Center \((-3,-2),\) focus \((-1,-2),\) and vertex \((1,-2)\)

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

Find an equation of an ellipse that satisfies the given conditions. Vertices \((\pm 3,2)\) and foci \((\pm 2,2)\)

Find an equation of an ellipse that satisfies the given conditions. Vertices \((-1, \pm 3)\) and foci \((-1, \pm 1)\)

Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. $$ 9 x^{2}+18 x+4 y^{2}-8 y-23=0 $$

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

Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. $$ 9 x^{2}-36 x+16 y^{2}-64 y-44=0 $$

Graph the parabola. Label the vertex, focus, and directrix. $$ \frac{1}{16}(x+4)^{2}=-(y-4) $$

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

Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. $$ 4 x^{2}+8 x+y^{2}+2 y+1=0 $$

Graph the parabola. Label the vertex, focus, and directrix. $$ x=2(y-2)^{2}-1 $$

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

Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. $$ 4 x^{2}+16 x+5 y^{2}-10 y+1=0 $$

Graph the parabola. Label the vertex, focus, and directrix. $$ -2(y+1)=(x+3)^{2} $$

Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. $$ 2 x^{2}+4 x+3 y^{2}-18 y+23=0 $$

Find an equation of a parabola that satisfies the given conditions. Sketch a graph of the parabola. Label the focus, directrix, and vertex. Focus \((0,2)\) and vertex \((0,1)\)

Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. $$ 16 x^{2}-16 x+4 y^{2}+12 y=51 $$

Find an equation of a parabola that satisfies the given conditions. Sketch a graph of the parabola. Label the focus, directrix, and vertex. Focus \((-1,2)\) and vertex \((3,2)\)

Write the equation in standard form for an ellipse centered at (h, k). Identify the center and the vertices. $$ 16 x^{2}+48 x+4 y^{2}-20 y+57=0 $$

Find an equation of a parabola that satisfies the given conditions. Sketch a graph of the parabola. Label the focus, directrix, and vertex. Focus \((0,0)\) and directrix \(x=-2\)

Graph the ellipse. $$ \frac{x^{2}}{15}+\frac{y^{2}}{10}=1 $$

Find an equation of a parabola that satisfies the given conditions. Sketch a graph of the parabola. Label the focus, directrix, and vertex. Focus \((2,1)\) and directrix \(x=-1\)

Graph the ellipse. $$ \frac{(x-1.2)^{2}}{7.1}+\frac{y^{2}}{3.5}=1 $$

Find an equation of a parabola that satisfies the given conditions. Focus \((-1,3)\) and directrix \(y=7\)

Graph the ellipse. $$4.1 x^{2}+6.3 y^{2}=25$$

Find an equation of a parabola that satisfies the given conditions. Focus \((1,2)\) and directrix \(y=4\)

Graph the ellipse. $$\frac{1}{2} x^{2}+\frac{1}{3} y^{2}=\frac{1}{6}$$

Find an equation of a parabola that satisfies the given conditions. Horizontal axis, vertex \((-2,3),\) passing through \((-4,0)\)

Solve the system of equations. Give graphical support by making a sketch. $$ \begin{aligned} &\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\\\ &x+y=3 \end{aligned} $$

Find an equation of a parabola that satisfies the given conditions. Horizontal axis, vertex \((-1,2),\) passing through \((2,3)\)

Solve the system of equations. Give graphical support by making a sketch. $$ \begin{aligned} &\frac{x^{2}}{16}+\frac{y^{2}}{25}=1\\\ &-2 x+y=5 \end{aligned} $$

Write the given equation either in the form \((y-k)^{2}=a(x-h)\) or in the form \((x-h)^{2}=a(y-k)\). $$ -2 x=y^{2}+6 x+10 $$