SOLUTION: Find the equation of the ellipse with vertices at (-2, 1) and (4, 1) with eccentricity 23.

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Question 1178761: Find the equation of the ellipse with vertices at (-2, 1) and (4, 1) with eccentricity 23.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Since the vertices are side by side , I know that this ellipse must be wider than it is tall. Then a^2 will go with the x part of the equation.
so, we need:
%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1
vertices at (-2,+1) and (4, 1)
distacnce between is 2a=6=>a=3
e+=+c%2Fa where a is the length of semi-major axis and c is the distance from centre to the foci
c%2Fa=2%2F3 =>+c=2 and a=3
b%5E2=a%5E2-c%5E2
b%5E2=3%5E2-2%5E2
b%5E2=9-4
b%5E2=5

the center is at (h, k) = half way between vertices, and k=1
then h=%28-2%2B4%29%2F2=1
the center is at (1, 1)
%28x-1%29%5E2%2F9%2B%28y-1%29%5E2%2F5=1