Question

Given a fixed circle C and a line L through the centre O of C. Take a variable point P on L and let K be the circle centre P through O. Let T be the point where a common tangent to C and K meets K. The locus of T is

• A. A circle
• B. A parabola
• C. A pair of straight lines
• D. None of these

Answer 1

Answer: (C)

A pair of straight lines

Answer 2

Let C be x² + y² – r² = 0 and k be x² + y² –2x = 0, a Ī

R. Let T be (h, k)

The equation of tangent to K at T(h, k) is

hx + ky – a (h + x) = 0

Ž $\frac{\alpha h}{\sqrt{(h - \alpha)^{2} + k^{2}}}$= r Ž h² – r² = 0