SOLUTION: center at the origin; a focus (0,2); vertex at (0,3)

Question 1186882: center at the origin; a focus (0,2); vertex at (0,3)
Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
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center at the origin; a focus (0,2); vertex at (0,3)
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The focus is closer to the center than the vertex ---> hence, the conic section is an ellipse.


A focus and a vertex lie on vertical line x= 0  ---> hence, the major axis is vertical.


The length of the major semi-axis is a = 3.


We find the length of the minor semi-axis b from the equation

    b = ,  where c is the eccentriciry  c= 2 (given).


So,  b =  =  = .


Thus the equation of the ellipse is


     +  = 1.

Solved.

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