find the locus of the following point

Question

let the fixed line $\frac{x}{a}+\frac{y}{b}=1$ cut the coordinate axis at two points $A$ and $B$, a variable line perpendicular to the life cuts the axes at $P$ and $Q$ respectively. Find the locus of point of intersection of the lines $AQ$ and $BP$.

Answer 1

The locus is the circle having $AB$ as a diameter.

We have that either $P$ is the orthocenter of $ABQ$, or $Q$ is the orthocenter of $ABQ$, hence $AQ$ and $BP$ are orthogonal.