Write the standard form of the conic equation in which Eccentricity = sqr(11)/4

Vertices: (0, 9+4(sqr 5)), (0, 9-4(sqr(5))

I have the answer of x^2 /25 + (y-9)^2 /80 = 1 but I don't understand how to get it. Thank you so much.

Write the standard form of the conic equation in which Eccentricity = sqr(11)/4

Vertices: (0, 9+4(sqr 5)), (0, 9-4(sqr(5))

I have the answer of x^2 /25 + (y-9)^2 /80 = 1 but I don't understand how to get it. Thank you so much.

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San Diego, CA

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.

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