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  4. Find the equation to the locus of a point which moves at a constant distance of 5 units from a fixed point (2,-3)

Q. Find the equation to the locus of a point which moves at a constant distance of $5$ units from a fixed point $(2,-3)$

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Solution:

given $\Rightarrow \cos 12 \theta-\cos \theta=20 \theta-\cos 2 \theta$
$\therefore \cos 20 \theta=\cos 12 \theta $
$\Rightarrow-2 \sin 16 \theta \sin 4 \theta=0$
$\therefore \sin 16 \theta=0$ or $\sin 4 \theta=0 $
$\therefore 16 \theta=n \pi, 4 \theta=n \pi $
$\therefore \theta=\frac{n \pi}{16}, $
$\theta=\frac{n \pi}{4}$

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