Answer
$(x+2)^2+(y+6)^2=25$
Work Step by Step
Center: $(h,k)=(-2,-6)$
Point on the circle: $(1,-10)$
The distance from the center to the solution point is the radius $r$ of the circle. Finding $r$ using the distance formula:
$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt {(-2-1)^2+[-6-(-10)]^2}=\sqrt {9+16}=\sqrt {25}=5$
Using the standard form of the equation of a circle:
$$(x−h)^2+(y−k)^2=r^2$$ $$[(x-(-2)]^2+[y-(-6)]^2=5^2$$ Simplifying:
$$(x+2)^2+(y+6)^2=25$$
