Write the equation of the circle with center (5, 1) and radius r = 10

The standard equation for the circle is:

(x-h)^2+(y-k)^2=r^2, where (h,k) is the center of the circle and r is the radius.

We are given that the center is (5,1) and r=10 so

(x-5)^2+(y-1)^2=100

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.