Answer
$x^{2}+y^{2}=65$
Work Step by Step
An equation of the circle with center $(h,k)$ and
radius $r$ is given as:
$(x-h)^{2}+(y-k)^{2}=r^{2}$
Given: center $(h,k)=(0,0)$ and $(x,y)=(4,7)$
Then
$(4-0)^{2}+(7-0)^{2}=r^{2}$
$r^{2}=65$
Hence, $x^{2}+y^{2}=65$