91Ó°ÊÓ

A planet's orbit about the Sun can be described as an ellipse. Consider the Sun as the origin of a rectangular coordinate system. Suppose that the \(x\) -intercepts of the elliptical path of the planet are \(\pm 130,000,000\) and that the \(y\) -intercepts are \(\pm 125,000,000 .\) Write the equation of the elliptical path of the planet.

Sketch the graph of each equation. If the graph is a parabola, find irs vertex. If the graph is a circle, find its center and radius. $$5 x^{2}+5 y^{2}=25$$

Comets orbit the Sun in elongated ellipses. Consider the Sun as the origin of a rectangular coordinate system. Suppose that the equation of the path of the comet is $$ \frac{(x-1,782,000,000)^{2}}{3.42 \cdot 10^{23}}+\frac{(y-356,400,000)^{2}}{1.368 \cdot 10^{22}}=1 $$ Find the center of the path of the comet.

Sketch the graph of each equation. If the graph is a parabola, find irs vertex. If the graph is a circle, find its center and radius. $$y=4 x^{2}-40 x+105$$

Sketch the graph of each equation. If the graph is a parabola, find irs vertex. If the graph is a circle, find its center and radius. $$y=5 x^{2}-20 x+16$$

Graph each equation. See Sections 3.2 and 3.3 $$y=2 x+5$$

Graph each equation. See Sections 3.2 and 3.3 $$y=-3 x+3$$

Sketch the graph \(\frac{(x-1)^{2}}{4}-\frac{(y+1)^{2}}{25}=1\)

Sketch the graph \(\frac{(x+2)^{2}}{9}-\frac{(y-1)^{2}}{4}=1\)

Graph each equation. See Sections 3.2 and 3.3 $$y=3$$