Word Problems with Ellipses

darshanpatel

1. The problem statement, all variables and given/known data

The Moon orbits the Earth in an elliptical path with the center of Earth at one focus. The major and minor axes of the orbit have lengths of 768,800 kilometers and 767,640 kilometers, respectively.

a) Find the greatest distance, called the apogee, and the lest distance, called the perigee, from Earth's center to the moon's center.

2. Relevant equations

-None-

3. The attempt at a solution

I tried sketching it out on a graph but I could get that far. I know for the least distance and greatest distance from the focus, it has to be right in front of the focus and behind it. Like you could connect them with a straight line on the ellipse. I think you need to use triangles, but not sure.

Mark44

You could or could not get that far? If you couldn't get that far, why not? A sketch of the ellipse should give you some insight into answering the questions here.
The apogee and perigee will be at the two vertices of the ellipse.

darshanpatel

Yeah I sketched it out but how would you get the distance from the focus to the vertex its closest too? It doesn't give a point to where Earth is...

Mark44

You're given the major and minor axes, from which you can get the major and minor semiaxes. How do these values relate to the parameters a and b in the equation of the ellipse? How do a and b relate to the number c, which represents the distance from the center to either focus?

Your textbook should have this information.

darshanpatel

I used c^2=a^2-b^2 to find the foci points, then used distance formula to find the shortest distance to the edge of the ellipse and subtracted that from the length of the major axis to find the longest distance....