Find an equation for the ellipse.

Question

center:(3,2) a=3c Foci:(1,2)(5,2)

h=3 k=2

I do not know where to start.

Answer 1

c is the distance from the centre to a focal point,
form (3,2) to (5,2) is 2
so c = 2, then a = 6
and we know in the ellipse,
c^2 + b^2 = a^2
4 + b^2 = 36
b^2 = 32

so
(x-3)^2 /36 + (y-2)^2/32 = 1