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write the standard form of conic equation

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1 Answer

Eccentricity= c/a=sqrt(11)/4
 
As per given vertices,major axis is vertical.
 
9+4sqrt(5)-9+4sqrt(5)=8sqrt(5)=2a
So,    a=4sqrt(5)
 
c/a=sqrt(11)/4. =c/4sqrt(5)
 
c=sqrt(55)
 
c^2= a^2. -b^2
 
55=80-b^2
b=5
 
Center coordinates=   (0,9)
 
Equation of ellipse is
 
[(x^2)/25]  + [(y-9)^2]/80=1
 
YOU are welcome to revert back if any step is not clear.