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(C) Let the midpoint of the variable chord be $P(h, k)$.The equation of the chord with midpoint $(h, k)$ for the circle $S: x^2 + y^2 - 2ax = 0$ is gi

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$x^2 + y^2 - ax = 0$

Vedclass · Answer

(C) Let the midpoint of the variable chord be $P(h, k)$.The equation of the chord with midpoint $(h, k)$ for the circle $S: x^2 + y^2 - 2ax = 0$ is given by $T = S_1$.$hx + ky - a(x + h) = h^2 + k^2 - 2ah$.Since the chord passes through the origin $(0, 0)$,we substitute $x = 0$ and $y = 0$ into the equation:$h(0) + k(0) - a(0 + h) = h^2 + k^2 - 2ah$.$-ah = h^2 + k^2 - 2ah$.$h^2 + k^2 - ah = 0$.Replacing $(h, k)$ with $(x, y)$,the locus is $x^2 + y^2 - ax = 0$.

$A$ 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:

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