Sketch a circle with center $(3, 5)$ and radius $4$ units. Label a point $P$ on the circle with the coordinates $(x, y)$.  

1. Write an expression for the distance between point $P$ and the center of the circle.

   Hint (a):

   Review the hint in part (b) of problem 10-6.

2. What is the exact distance between any point on your circle and the center of the circle? Use this distance with your expression from part (a) to write an equation and then simplify the result.

   Hint: (b):

   The distance between any point on a circle and its center is the radius.