Hello, rpatel!

Here's the first part.

I'll try to get back to the rest later . . .

There are a number of approaches to this problem.(a) Find the equation of the circle that passes through A(2,3), B(0,-1), C(-4,-3).

What is the center and radius of this circle?

I think this one is the simplest. (I may be the only one!)

The center is the point equidistant from

Equate the distances: .

. .

From , we have: .

From , we have: .

Solve the system of equations: .

. . Hence, the center is: .

The radius is the distance ... (or or

. .

Therefore, the equation of the circle is:

. .