The curve represents a vertical ellipse with centre ,(h,k)= (5,7), length of major axis,2a=6 units , that gives a=3 and length of minor axis, 2b = 2 units, that gives b=1
The equation of vertical ellipse is
[tex] \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1 [/tex]
And on substituting the values of h,k , a and b, we will get
[tex] \frac{(x-5)^2}{1}+\frac{(y-7)^2}{9}=1 [/tex]
And that's the required equation .
