Question

A variable chord is drawn through the origin to the circle $x^2+y^2-2ax=0$. Locus of the centre of the circle drawn on this chord as diameter is

• A. $x^2+y^2+ay=0$
• B. $x^2+y^2-ay=0$
• C. $x^2+y^2-ax=0$
• D. $x^2+y^2+ax=0$

Answer 1

The correct option is C $x^2+y^2-ax=0$

$S_1=S_{11}$ is passing through origin
$x{x}_1+y{y}_1-a(x+x_1)=x_1^2+y_1^2-2a{x}_1$ is passing through (0, 0)
Which gives , $x_1^2+y_1^2-a{x}_1=0$ Generalizing $(x_1,y_1)$ with (x,y)
Hence locus is $x_1^2+y_1^2-a{x}_1=0$