Let be a given circle. The locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin is
Let lx + my = 1 ...(1)
be a chord of the circle
...[A]
It subtends a right angle at the origin.
∴ The lines joining the origin to the points of intersection of chord and circle are at right angles. Making (A) homogeneous with the help of (1).
...[2]
A line through the origin and perpendicular to (1) is
mx – ly = 0 ...(3)
....[4]
Substituting values of l and m in (2), we get
Study 40% syllabus and score up to 100% marks in JEE