Equal Chords from Perpendicular Lines

In the coordinate plane $xOy$, consider the circles

1. A line $l$ through the point $A(-4,0)$ meets the circle $C_1$; among all such lines, the longest chord cut on $C_1$ is $AB$ and the shortest is $CD$. Find the area of the quadrilateral $ABCD$. 2. Let $P$ be a point of the plane with the following property: there exist infinitely many pairs of perpendicular lines $l_1$ and $l_2$ through $P$ such that $l_1$ meets $C_1$, $l_2$ meets $C_2$, and the chord cut by $l_1$ on $C_1$ has the same length as the chord cut by $l_2$ on $C_2$. Find the coordinates of all such points $P$.