$r=6$  

$P=\left(4,y_1\right),y_1>0$  

$R=\left(4,y_2\right),y_2<0$

$6^2=4^2+y^2$  

$36=16+y^2$  

$y^2=20$  

$y_1=\sqrt{20}{y}_2=-\sqrt{20}$

$y_1=2\sqrt{5}{y}_2=-2\sqrt{5}$            

$P=\left(4,2\sqrt{5}\right)$  

$R=\left(4,-2\sqrt{5}\right)$