Question

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

Answer 1

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