Question

write an equation for a circle with the given conditions

area of 36 pi & a center at point (4,7)

Answer 1

you can calculate radius r by
\[\pi r^2= 36 \pi\]
and after that use eqn of circle \[(x-a)^2 +(y-b)^2 =r^2\]
where (a,b)=(4,7)

Answer 2

as @gyanu said
using the Area of a Circle, solve for "r" to get the radius, once you get the radius
you're already given the center of the circle
and that's all you need for the circle's equation, thus just plug them all in :) like so -> http://www.mathwarehouse.com/geometry/circle/images/equation-of-circle/example-2-equation-of-circle.png