Find the value of $a^2+p^2$, given that $F_1$ is the focus of $(y-a)^2=4px$ and $F_2$ is the focus of $y^2=-4x$, $F_1F_2=3$ and $PQ=1$ where $P$ is the intersection of line $F_1F_2$ on $(y-a)^2=4px$ and $Q$ is the intersection of line $F_1F_2$ on $y^2=-4x$ .
My approach is as follow $F_1:(p,a)$ and $F_2:(-1,0)$, $F_!F_2=\sqrt{(p+1)^2+a^2}=3$. The parametric equation of $y^2=-4x$ is $x=-t$ and $y=2t$ where $t>0$. Line $F_1F_2:y+1=-\frac{2t}{t-1}x$ and final relation is $a+1=-\frac{2t}{t-1}p$.
How do I proceed from here