SOLUTION: Find the equation of the ellipse whose center is at (-3-1), vertex at (2,-1), and focus at (1,-1)

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Question 1161785: Find the equation of the ellipse whose center is at (-3-1), vertex at (2,-1), and focus at (1,-1)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The major axis is horizontal, so....

the standard form of the equation is %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2+=+1

The center is at (h,k)
a is the length of the semi-major axis
b is the length of the semi-minor axis
c is the distance from the center to the focus
c%5E2+=+a%5E2%2Bb%5E2

The given information tells us....

(h,k) = (-3,-1)
a = 2-(-3) = 5
c = 1-(-3) = 4

Use the known values of a and c to determine b; then plug all the right numbers in the standard form.