Let the tangent to the curve x^2+2 x-4 y+9=0 at the point P (1,3) on it meet the y -axis at A. Let the line passing through P and parallel to the…

Let the tangent to the curve $\displaystyle x^2+2 x-4 y+9=0$ at the point $\displaystyle \mathrm{P}(1,3)$ on it meet the $\displaystyle y$-axis at A . Let the line passing through P and parallel to the line $\displaystyle x-3 y=6$ meet the parabola $\displaystyle y^2=4 x$ at B . If B lies on the line $\displaystyle 2 x-3 y=8$, then $\displaystyle (\mathrm{AB})^2$ is equal to $\displaystyle \_\_\_\_$