The diameter of a circle has endpoints p(-7,-10)and q(3,2). find the center of the circle. find the radius. if your answer is not an integer, express it in radical form. write an equation for the circle

Since we have the endpoints of a diameter the center is very easy to find.  It is the midpoint of the diameter endpoints, which is just the average coordinates...

The center is:

((-7+3)/2, (-10+2)/2)

(-2,-4)

To find the radius we can use the endpoints again to find the diameter squared and then get the radius from that:

d^2=(dy)^2+(dx)^2

d^2=(2--10)^2+(3--7)^2

d^2=12^2+10^2

d^2=144+100

d^2=244

d=√244, since d=2r, r=d/2

r=√(244/4)

r=√61

The equation of a circle is (x-h)^2+(y-k)^2=r^2.  We found earlier that the center was at (-2,-4) and we just saw that r^2=61 so:

(x+2)^2+(y+4)^2=61