SOLUTION: The ellipse has its center at the origin, a=2, and e=3/4. Write the equation of the ellipse.

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Question 726873: The ellipse has its center at the origin, a=2, and e=3/4.
Write the equation of the ellipse.
Answer by lwsshak3(11628) About Me  (Show Source):
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The ellipse has its center at the origin, a=2, and e=3/4.
Write the equation of the ellipse.
***
center:(0,0)
a=2
a^2=4
e=3/4=c/a
c=3a/4=6/4=3/2
c^2=9/4
b^2=a^2-c^2=4-9/4=36/4-9/4=27/4
This is an ellipse with vertical major axis.
Its standard form: %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1, a>b, (h,k)=(x,y) coordinates of center.
Equation of given ellipse:
x%5E2%2F4%2By%5E2%2F%2827%2F4%29=1