Question

P,Q,R and S are the points of intersection with the co - ordinate axes of the lines $ax+by=abandbx+ay=ab$, then P,Q,R,S are concyclic.

Answer 1

On dividing by ab the equation of lines can be re-written as $\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{b}+\frac{y}{a}=1$. Clearly product of intercepts on x-axis = product of intercepts on y-axis each equal to ab. Hence P,Q,R,S are concylic