Answer
$(x+1)^2+(y-2)^2=25$
Work Step by Step
The distance formula from $A(x_1,y_1)$ to $B_2(x_2,y_2)$ can be written as:
$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$
The distance between the center and $(3, 5)$ is the radius $r$.
Thus, using the distance formula gives:
$r=\sqrt{(5-2))^2+(3-(-1))^2}=\sqrt{9+16}=\sqrt{25}=5$
The standard form for a circle with radius $r$ and center $(h,k)$ can be written as:
$$(x-h)^2+(y-k)^2=r^2$$
Thus, the equation of the circle whose center is at $(-1,2)$ and contains the point $(3, 5)$ is:
$$(x+1)^2+(y-2)^2=5^2\\
(x+1)^2+(y-2)^2=25$$
