91Ó°ÊÓ

Find an equation of an ellipse for each given height and width. Assume that the center of the ellipse is \((0,0) .\) $$ h=40 \mathrm{mi}, w=60 \mathrm{mi} $$

Find the foci of each hyperbola. Then draw the graph. $$ 4 y^{2}-25 x^{2}=100 $$

Identify the focus and the directrix of the graph of each equation. $$ y=\frac{1}{4} x^{2} $$

Write an equation for each translation. $$ x^{2}+y^{2}=50 ; \text { right } 5 $$

Identify the conic section represented by each equation by writing the equation in standard form. For a parabola, give the vertex. For a circle, give the center and the radius. For an ellipse or a hyperbola, give the center and the foci. Sketch the graph. \(y^{2}-x^{2}+6 x-4 y=6\)

Find an equation of an ellipse for each given height and width. Assume that the center of the ellipse is \((0,0) .\) $$ h=5 \mathrm{m}, w=2 \mathrm{m} $$

Identify the conic section represented by each equation by writing the equation in standard form. For a parabola, give the vertex. For a circle, give the center and the radius. For an ellipse or a hyperbola, give the center and the foci. Sketch the graph. \(x^{2}-4 y^{2}-2 x-8 y=7\)

Identify the focus and the directrix of the graph of each equation. $$ y=x^{2} $$

Find the foci of each hyperbola. Then draw the graph. $$ 36 x^{2}-8 y^{2}=288 $$

Identify the focus and the directrix of the graph of each equation. $$ y=-\frac{1}{8} x^{2} $$