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Let a given line {L}_{{{1}}} intersects the {x}- and y-axes at

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Let a given line $L_{1}$ intersects the $x -$ and y-axes at P and Q, respectively. Let another line $L_{2}$ , perpendicular to $L_{1}$ , cuts the x- and the y-axis at R and S, respectively. Show that th elocus of the point of intersection of the line PS and QR is a circle passing through the origin.

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Let a given line

L_{1}

intersects the

x -

and y-axes at P and Q, respectively. Let another line

L_{2}

, perpendicular to

L_{1}

, cuts the x- and the y-axis at R and S, respectively. Show that th elocus of the point of intersection of the line PS and QR is a circle passing through the origin.

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