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Equation of a Chord Joining Two Points with Circle in Parametric Form

The locus of ...

Question

The locus of the mid points of the chords of the circle $x^{2} + y^{2} + 4 x - 6 y - 12 = 0$ which subtend and angle of radians at its circumference is

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Solution

The correct option is B

C = (-2, 3)

r = 5

$c o s \frac{π}{6} = \frac{c p}{5} \Rightarrow C P^{2} = 25 c o s^{2} \frac{π}{6} (x + 2)^{2} + (y - 3)^{2} = \frac{75}{4}$

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