Answer:
(9,-5)
Step-by-step explanation:
The equation of an ellipse can be represented as
[tex]\frac{(x-h)^{2} }{b^{2}} +\frac{(y-k)^{2}}{a^{2}} =1[/tex]
where (h,k) is the center.
In [tex]\frac{(y+5)^{2}}{121} +\frac{(x-9)^{2}}{49} =1[/tex]
We can see the h and k values are 9 and -5 respectively, so the center is (9,-5)
The center of the ellipse is ( -5,9)
Ellipse is an oval shaped plane curve , it is drawn such that the sum of the distances of all the points from the two focal points is constant.
The equation of ellipse given is
(y+5)²/121+(x-9)²/49=1
The standard equation of ellipse with ( h,k) as center is
[tex]\dfrac{(x-h)^2}{a^2} +\dfrac {(y-k)^2}{b^2} = 1[/tex]
The given equation (y+5)²/121+(x-9)²/49=1 can be written as
(y+5)²/11² +(x-9)²/7²=1
On comparing the given and standard equation ,
h = -5 , k = 9
Therefore the center of the ellipse is ( -5,9)
To know more about Ellipse
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