analytic geometry question

• Mar 5th 2008, 10:01 PM
bluebirdsfly
analytic geometry question
The perimeter of a triangle is 30, and the points (0,-5) and (0,5) are two fo the vertices. Find the equation of the ellipse of the third vertex.

Any idea as to how to begin solving this problem...?
• Mar 6th 2008, 05:17 AM
earboth
Quote:

Originally Posted by bluebirdsfly
The perimeter of a triangle is 30, and the points (0,-5) and (0,5) are two fo the vertices. Find the equation of the ellipse of the third vertex.

Any idea as to how to begin solving this problem...?

An ellipse is the locus of all points which have the constant sum of distances from 2 fixed points (=focus).

Therefore:
1. (0, -5), (0, 5) are the focii.
2. The sum of distances is 20. (The distance between the focii is 10!)
3. The length of the main semiaxis must be 10.
4. The center of the ellipse must be the origin.
5. The length of the minor semi axis must be:$\displaystyle b = \sqrt{10^2-5^2} = 5 \cdot \sqrt{3}$
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