Suppose AB is the diameter of a circle, where A = (-1,-3) and B = (3,-2). The equation of the circle is?
4(x-1)^2 +4(y+5/2)^2 =17
I will give you the steps. I will not do your homework for you.
1)Find the midpoint between $\displaystyle A(-1,-3) \mbox{ and }B(3,-2)$. Use the midpoint formula (see below).
2)The answer to #1 is the center of circle.
3)Find the length between $\displaystyle A(-1,-3)\mbox{ and }B(3,-2)$. Use the distance formula (see below).
4)The answer to #4 is diamter length, find half of it.
5)You know the center of circle and its radius. You can now describe its equation.
---
Midpoint formula: $\displaystyle \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)$
Distance formula: $\displaystyle \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$