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(B) Let the points be $A(5, 0)$ and $B(10 \cos 	heta, 10 \sin 	heta)$.Using the section formula,the coordinates of point $P(x, y)$ dividing $AB$ in

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(B) Let the points be $A(5, 0)$ and $B(10 \cos 	heta, 10 \sin 	heta)$.Using the section formula,the coordinates of point $P(x, y)$ dividing $AB$ in the ratio $2 : 3$ are:$x = \frac{2(10 \cos 	heta) + 3(5)}{2 + 3} = \frac{20 \cos 	heta + 15}{5} = 4 \cos 	heta + 3$$y = \frac{2(10 \sin 	heta) + 3(0)}{2 + 3} = \frac{20 \sin 	heta}{5} = 4 \sin 	heta$From these equations,we have:$x - 3 = 4 \cos 	heta \implies \cos 	heta = \frac{x - 3}{4}$$y = 4 \sin 	heta \implies \sin 	heta = \frac{y}{4}$Using the identity $\cos^2 	heta + \sin^2 	heta = 1$,we get:$(\frac{x - 3}{4})^2 + (\frac{y}{4})^2 = 1$$(x - 3)^2 + y^2 = 16$This is the equation of a circle with center $(3, 0)$ and radius $4$.

$A$ point $P(x, y)$ divides the line segment joining the points $(5, 0)$ and $(10 \cos \theta, 10 \sin \theta)$ in the ratio $2 : 3$. Find the locus of point $P$ as $\theta$ varies.

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