Question

The point (-9,-7) is on a circle with center (8,4). write in standard equation of the circle.

Answer 1

The standard form of the circle is:

(x-h)^2+(y-k)^2=r^2, where (h,k) is the center of the circle and r is its radius...

We are given the center is (8,4) so we have:

(x-8)^2+(y-4)^2=r^2

So we now have to find the radius.  Since (-9,-7) is on the circle and the center is (8,4), the distance between these two points is equal to the radius...

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

r^2=(8--9)^2+(4--7)^2

r^2=17^2+11^2

r^2=289+121

r^2=410  so now we have the complete standard equation for this circle:

(x-8)^2+(y-4)^2=410