Locus problem solve it using simple mathematics

Question

A line cuts $X$-axis at $A(7,0)$ and the $Y$- axis at $B(-5,0)$. A variable line $PQ$ is drawn perpendicular to $AB$ cutting $X$-axis at $P$ and $Y$-axis at $Q$. If $AQ$ and $BP$ intersect at $R$, Find locus of $R$.

Answer 1

$PQ$ is perpendicular to $AB$, $AP$ is perpendicular to $BQ$, hence $BP$ is perpendicular to $AQ$ (fairly trivial to demonstrate), and the angle $\angle BRA$ is a right angle.

The locus of $R$ is the figure that sees two points at a right angle... It is the circle of diameter $AB$.