Question

State the equation of a circle which has a center at (2,2) and passes through the point(4,4)

Answer 1

The equation of a circle of radius r centered at the origin is x^2 + y^2 = r^2.
What's the eq. of a circle of radius r centered at the point (h,k)?
Once you've got that equation, substitute the known info, that is, h=2, k=2, x=4, y=4. This will result in a value for the radius, r.
Then write the equation of this circle, using the given and the calculated center and radius.