Answer
$x_{1}= 0 ;y_{1}=\sqrt{27}+1$
$x_{2}= 0;y_{2}=-\sqrt{27}+1$
Work Step by Step
The two points are on the y axis, so
$x_{1}=x_{2}=0$
Using the Distance Formula we can calculate the distances.
$6 = \sqrt{(0-3)^{2}+(y-1)^{2}} = \sqrt{9+(y-1)^{2}}$
$9+(y-1)^{2}=36$
$(y-1)^{2}=27$
$(y-1) = \pm\sqrt{27}$
$y=\pm\sqrt{27}+1$
$y_{1}=\sqrt{27}+1$
$y_{2}=-\sqrt{27}+1$
