What is the equation of a circle with its center at (3,5) and an area of 36pi?

equation of a circle centre (a,b) with radius r has equation

(x-a)^2 +(y-b)^2=r^2

 

Your circle has equation (x-3)^2 + (y-5)^2 = r^2.

 

Now to find r for your circle.  Area of circle =(pi)r^2 = 36(pi)

                                                       so                r^2  = 36

radius of your circle is                                        r      = 6

 

full equation of your circle is (x-3)^2 = (y-5)^  = 36