__Question 1:__

The general equation of a circle is given by $\displaystyle (x-m)^2 + (x-n)^2 = r^2$, whereby $\displaystyle (m,n)$ is the circle's midpoint.

Step 1: Find the midpoint. $\displaystyle (m,n)=\left(\tfrac{x_2+x_1}{2},\tfrac{y_2+y_1}{2})$

Step 2: Compute the distance, $\displaystyle d$, between the two diameter endpoints. This gives the diameter, which is twice the radius.$\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step 3: Plug it all in.$\displaystyle (x-m)^2 + (x-n)^2 = (\tfrac{d}{2})^2$