Question 1186882
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center at the origin; a focus (0,2); vertex at (0,3)
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<pre>
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 = {{{sqrt(a^2 - c^2)}}},  where c is the eccentriciry  c= 2 (given).


So,  b = {{{sqrt(3^2 - 2^2)}}} = {{{sqrt(9-4)}}} = {{{sqrt(5)}}}.


Thus the equation of the ellipse is


    {{{x^2/5}}} + {{{y^2/9}}} = 1.
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Solved.