#### Answer

$\color{blue}{x^2+y^2=34}$

#### Work Step by Step

RECALL:
The center-radius form of a circle whose center is at $(h, k)$ and whose radius is $r$ units is:
$(x-h)^2+(y-k)^2=r^2$
The given circle has its center at $(0, 0)$
Thus, the tentative equation of the circle is :
$(x-0)^2+(y-0)^2=r^2
\\x^2+y^2=r^2$
To find the value of $r^2$, substitute the x and y values of the point $(3, 5)$ to obtain:
$3^2+5^2=r^2
\\9+25=r^2
\\34=r^2$
Therefore, the equation of the circle is:
$\\\color{blue}{x^2+y^2=34}$