Search
Ask a question
0 0

write the standard form of conic equation

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.
Tutors, please sign in to answer this question.

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.