The locus of the middle point of the chord of the circle $x^{2} + y^{2} - 12 x + 4 = 0$ , that subtends an angle $\frac{2 π}{3}$ at the centre is

x^{2} + y^{2} - 12 x + 4 y + 30 = 0

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x^{2} + y^{2} - 12 x + 4 y + 31 = 0

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x^{2} + y^{2} + 12 x + 4 y + 30 = 0

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x^{2} + y^{2} - 12 x + 28 = 0

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Solution

The correct option is D $x^{2} + y^{2} - 12 x + 28 = 0$
$\begin{matrix} cos \frac{π}{3} = \frac{C B}{C A} = \frac{C B}{4 \sqrt{2}} \frac{1}{2} = \frac{C B}{4 \sqrt{2}} C B = 2 \sqrt{2} {(h - 6)}^{2} + k^{2} = 8 x^{2} + y^{2} - 12 x + 28 = 0 H e n c e, t h e o p t i o n D i s t h e c o r r e c t a n s w e r . \end{matrix}$

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