JEE Advance - Mathematics (1987 - No. 17)
Let a given line $$L_1$$ intersects the x and y axes at P and Q, respectively. Let another line $$L_2$$, perpendicular to $$L_1$$, cut the x and y axes at R and S, respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.
The locus is a circle because the angle subtended by the line segment joining (0,0) and the point of intersection at P and Q is a right angle.
The locus is a circle because PS and QR are always perpendicular.
The locus is a circle because the intersection point is equidistant from the origin.
The locus is a circle because the equation of the locus can be simplified to the form x^2 + y^2 + 2gx + 2fy + c = 0, with c=0.
The locus is a circle because lines PS and QR intersect at right angle, so the point must lie on circle.
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