SOLUTION: Find an equation for the ellipse. foci at (-9,0) and (9,0)​; y​-intercepts are -4 and 4

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Question 1154219: Find an equation for the ellipse.
foci at (-9,0) and (9,0)​; y​-intercepts are -4 and 4

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The formula generally associated with the focus of an ellipse is c%5E2=a%5E2-b%5E2 where c is the distance from the focus to center , a is the distance from the center to a vetex and b is the distance from the center to a co-vetex.
if foci at (-9,0) and (9,0), we know that c=9 and center is at origin
if y​-intercepts are -4 and 4, co-vetices are at (0,-4) and (0,4) => b=4
use c%5E2=a%5E2-b%5E2 to calculate a
9%5E2=a%5E2-4%5E2
9%5E2%2B4%5E2=a%5E2
81%2B16=a%5E2
97=a%5E2

formula you will need is
x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1...plug in a%5E2 and b%5E2

x%5E2%2F97%2By%5E2%2F16=1