circle at center at (h,k) and radis r is
(x-h)^2+(y-k)^2=r^2
r=10
(0,0) is center
(x-0)^2+(y+0)^2=10^2
x^2+y^2=100
test them
(-6,4)
x=-6 and y=4
36+16=42, not 100
not on it
sqrt 10 and sqrt10
10+10=20, not 100
(6,-8)
36+64=100
correct
answer is (6,-8)
