It's your turn on distance and circles

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf file below.

Exercise 1.

Find the equation of the circle passing through (A=(2,-1)), (B=(-2,3)), (C=(0,5)) and compute its center and its radius.

Exercise 2.

For which values of the parameter (k) does the equation (3x^2+3y^2-4x+6y-k=0) represent a circle? For each of these values of the parameter, compute the center and the radius of the obtained circle.

Exercise 3.

Find the equation of the circle of center (C=(5,-1)) and passing through (A=(-2,3)).