Question

A line cuts the x-axis at A(4, 0) and the y-axis at B(0, 8). A variable line PQ is drawn perpendicular to AB cutting the x-axis in P and the y-axis in Q. If AQ and BP intersect at R, find the locus of R.

• A. $x^2+y^2-2x-4y=0$
• B. $x^2+y^2+2x+4y=0$
• C. $x^2+y^2-2x+4y=0$
• D. $x^2+y^2-4x-8y=0$

Answer 1

The correct option is D

$x^2+y^2-4x-8y=0$

$\angle ARB=\frac{\pi }{2}$
The locus is equation of the circle having A, B as end points of diameter i.e $x^2+y^2-4x-8y=0$