Q. A line through (0, 0) cuts the circle $x^{2} + y^{2} - 2ax = 0$ at $A$ and $B$, then locus of the centre of the circle drewn $AB$ as diameter is
A) $x^{2} + y^{2} - 2ay = 0$
B) $x^{2} + y^{2} + ay = 0$
C) $x^{2} + y^{2} + ax = 0$
D) $x^{2} + y^{2} - ax = 0$
Explanation
(d)
Let $AB$ is a chord and its equation is $y = mx$ …(i)
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Equation of $CM$ which is perpendicular to $AB$, is
$x + my = \lambda$
It passes through the centre $(a,\ 0)$
$\Rightarrow x + my = a$ …(ii)
On eliminating $m$ from Eqs. (i) and (ii), we get
$x^{2} + y^{2} = ax$
$\Rightarrow x^{2} + y^{2} - ax = 0$ is the locus of the centre of the required circle
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.