The locus of a point P which divides the line | vedclass

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(B) Let the coordinates of the point $P(h, k)$ divide the line segment joining $(1, 0)$ and $(2\cos 	heta, 2\sin 	heta)$ in the ratio $2 : 3$.Using

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Circle

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(B) Let the coordinates of the point $P(h, k)$ divide the line segment joining $(1, 0)$ and $(2\cos 	heta, 2\sin 	heta)$ in the ratio $2 : 3$.Using the section formula,we have:$h = \frac{2(2\cos 	heta) + 3(1)}{2 + 3} = \frac{4\cos 	heta + 3}{5}$$k = \frac{2(2\sin 	heta) + 3(0)}{2 + 3} = \frac{4\sin 	heta}{5}$From these,we get:$\cos 	heta = \frac{5h - 3}{4}$ and $\sin 	heta = \frac{5k}{4}$Using the identity $\cos^2 	heta + \sin^2 	heta = 1$,we substitute the values:$\left(\frac{5h - 3}{4}ight)^2 + \left(\frac{5k}{4}ight)^2 = 1$$(5h - 3)^2 + (5k)^2 = 16$Replacing $(h, k)$ with $(x, y)$,the locus is $(5x - 3)^2 + (5y)^2 = 16$,which represents a circle.

The locus of a point $P$ which divides the line joining $(1, 0)$ and $(2\cos \theta, 2\sin \theta)$ internally in the ratio $2 : 3$ for all $\theta$ is a

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