1. Equation of a circle

A(4,3) and B(-4,-3) are the endpoints of the diameter of a circle. Determin the center of the circle and the equation of the circle.
I found the center as (0,0) by using the midpoint formula.
where do i go from here?

2. Recall the equation of a circle: $\displaystyle (x - h)^{2} + (x - k)^{2} = r^{2}$

where $\displaystyle (h,k)$ is the coordinate of circle's centre and $\displaystyle r$ (not $\displaystyle r^2$) is your radius.

You have your centre and you can easily find the radius via the pythagorean theorem (draw a line to the coordinate (4,3) and a right-angled triangle can be constructed) or the distance formula. Whichever.