Question

What is the equation of the circle with center (-6,7) that passes through the point (4,-2). A. (x+6)^2+(y-7)^2=181 B. (x-6)^2+(y+7)^2=181 C. (x+6)^2+(y-7)^2=9 D. (x-6)^2+(y+7)^2=9

Answer 1

The equation of a cricle passing through (h,h) and with radius r is
$(x-h)^2+(y-k)^2=r^2$
so

cente ris (-6,7) and passing through (4,-2)
$(x-(-6))^2+(y-7)^2=r^2$
$(x+6)^2+(y-7)^2=r^2$
subsitute (4,-2) to find r^2

$(4+6)^2+(-2-7)^2=r^2$
$(10)^2+(-9)^2=r^2$
$100+81=r^2$
$181=r^2$

so it is

$(x+6)^2+(y-7)^2=181$
A is the answer