A parabola has been created with a string construction from the control points, $A$, $B$ and $C$. $A = (2, 12)$ $B = (2, 2)$ $C = (12, 2)$ Point $Q$ is on the line $AB$ at $(2, 6)$. Point $R$ is on the line $BC$ at $(8, 2)$. Line $QR$ touches the parabola at point $P$.  Given that the ratio of $AQ : AB$ equals the ratio of $BR : BC$, what are the coordinates of $P$? $P$ = $($[[☃ numeric-input 1]], [[☃ numeric-input 2]]$)$