91Ó°ÊÓ

In the following exercise, graph the equation$\frac{x^2}{25}+\frac{y^2}{36}=1$

In the following exercise, graph the equation$x=4{\left(y+1\right)}^2-4$

In the following exercise, graph the equation$x^2+y^2=64$

In the following exercise, graph the equation$\frac{x^2}{9}+\frac{y^2}{25}=1$

In the following exercises, simplify each expression.

${\left(y^4\right)}^3.{\left(y^5\right)}^2$

In the following exercise, graph the equation$y=6x^2+2x-1$

In the following exercise, graph the equation$\frac{{\left(x-2\right)}^2}{9}+\frac{{\left(y+3\right)}^2}{25}=1$

A planet moves in an elliptical orbit around its sun. The closest the planet gets to the sun is approximately 10 AU and the furthest is approximately 30 AU. The sun is one of the foci of the elliptical orbit. Letting the

ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the planet.

In the following exercise-$(-2,-6)and(6,-2)$

(a) find the midpoint of the line segments whose endpoints are given and,

(b) plot the endpoints and the

midpoint on a rectangular coordinate system.

A planet moves in an elliptical orbit around its sun. The closest the planet gets to the sun is approximately 10 AU and the furthest is approximately 70 AU. The sun is one of the foci of the elliptical orbit. Letting the

ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the planet.