A Algebraic Word Problem (Elipses)

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A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius of 519 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 230 km to 138 km.
 


Draw a circle centered at the origin. This circle has a radius of 519.

Draw an ellipse around the circle.

Where the ellipse crosses the y-axis, make it come close to the circle. Let the ellipse get a little farther away from the circle, where it crosses the x-axis.

The distance between the y-intercepts of the ellipse and the circle is 138.

The distance between the x-intercepts of the ellipse and the circle is 230.

In other words, on the ellipse, the coordinates of the y-intercept between quadrants I and II are (0, 657), and the coordinates of the x-intercept between quadrants I and IV are (749, 0).

Do you know how to write the equation for an ellipse, given the lengths of the major and minor axes?

 
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