Answer
$x = 5~cos~t+3$
$y = 5~sin~t+4$
where $t$ in $[0,2\pi]$
Work Step by Step
We can find $r$:
$r = \sqrt{3^2+4^2} = \sqrt{25} = 5$
We can write parametric equations for a circle of radius 5 centered on the origin:
$x = r~cos~t = 5~cos~t$
$y = r~sin~t = 5~sin~t$
where $t$ in $[0,2\pi]$
For the circle to be centered on the point (3,4), the x-values must be translated 3 units in the positive x-direction, and the y-values must be translated 4 units in the positive y-direction.
We can write parametric equations for a circle of radius 5 centered on the point (3,4):
$x = 5~cos~t+3$
$y = 5~sin~t+4$
where $t$ in $[0,2\pi]$
