Find an equation for the conic section with the given proper

Find an equation for the conic section with the given properties. The ellipse with foci F1(3, 2) and F2(7, 2) that passes through the point (5, 1)

foci F1(3, 2) and F2(7, 2)

centre = ( 5, -2)

that passes through the point (5, 1)

distance between focus (5 units)

b^2 = a^2 -c^2

a^2 -b^2 = c^2 ----> a^2 -b^2 = 25----(1)

passe through (5,1) : (x- 5)^2/a^2 +(y+2)^2/b^2 =1

0 +(1+2)^2/b^2 =1

b^2 = 9

a^2 -9 = 25 ---> a^2 = 34

So, equation of ellipse : (x- 5)^2/34^2 +(y+2)^2/9^2 =1