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 $BP$.
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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.
Jack D'Aurizio
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what is its radius??rather what is the equation of the locus, i got it as x^2 + y^2=ax+by – Archit Nanda Sep 12 '14 at 18:20
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@ArchitNanda: if AB is a diameter, can you guess what is the radius? – Jack D'Aurizio Sep 12 '14 at 18:53