Q. A variable chord is drawn through the origin to the circle$x^{2} + y^{2} - 2ax = 0$. The locus of the centre of the circle drawn on this chord as diameter is
A) $x^{2} + y^{2} + ax = 0$
B) $x^{2} + y^{2} - ax = 0$
C) $x^{2} + y^{2} + ay = 0$
D) $x^{2} + y^{2} - ay = 0$
Explanation
(b)
Let $(h,\ k)$ be the coordinates of the centre of circle of which the given chord is the diameter.
Then, $(h,\ k)$ be mid point of the chord, so, its equation is $S^{'} = T$
$h^{2} + k^{2} - 2ah = hx + ky - a(x + h)$
$\Rightarrow \ \ x(h - a) + ky = h^{2} + k^{2} - ah$
If it passes through (0, 0), therefore $h^{2} + k^{2} - ah = 0$ and the locus of $(h,\ k)$ is $x^{2} + y^{2} - ax = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.