Question

If the locus of midpoints of the chords of the circle \[ S\equiv x^2+y^2-6x-8y-11=0 \] which subtend a right angle at \(A(1,2)\) is another circle \(S'=0\), then the centre of \(S'=0\)

• A. is the midpoint of the line segment joining \(A\) and the centre of \(S=0\)
• B. Divides the line segment joining \(A\) and the centre of \(S=0\) in the ratio \(1:2\)
• C. Lies outside the circle \(S=0\)
• D. A vertex of the triangle having \(A\) and the centre of \(S=0\) as other two vertices

Hint:

For a fixed point \(P\), the locus of the midpoints of the chords of a circle subtending a right angle at \(P\) is another circle whose centre is the midpoint of the line joining \(P\) and the centre of the given circle.

Answer 1

The Correct Option is A