SOLUTION: Find the equation of an ellipse if the major axis is 8 units and the foci are (2, 3) and (2, -3).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of an ellipse if the major axis is 8 units and the foci are (2, 3) and (2, -3).      Log On


   

Question 752067: Find the equation of an ellipse if the major
axis is 8 units and the foci are (2, 3) and (2, -3).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Major axis is vertical based on "foci are (2, 3) and (2, -3)." The equation will be like this:
%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1.

2%2Aa=8 so meaning a=4.

Again using foci are (2, 3) and (2, -3), c=3.

You also see that the center of the ellipse from the focal information is at (2,0), so the equation can be seen as:
%28x-2%29%5E2%2Fb%2By%5E2%2F16=1----------Almost done.

Are you aware that the relationship amoung a, b, and c, is a%5E2=b%5E2%2Bc%5E2 ? Use this to find b and finish the equation.