Let A = (0, 4) and B = (2 cos theta, 2 sin th | vedclass

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(C) Given $A = (0, 4)$ and $B = (2 \cos 	heta, 2 \sin 	heta)$.$P$ divides $AB$ in the ratio $2:3$ internally.Using the section formula,the coordinat

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circle

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(C) Given $A = (0, 4)$ and $B = (2 \cos 	heta, 2 \sin 	heta)$.$P$ divides $AB$ in the ratio $2:3$ internally.Using the section formula,the coordinates of $P(x, y)$ are:$x = \frac{2(2 \cos 	heta) + 3(0)}{2 + 3} = \frac{4 \cos 	heta}{5} \Rightarrow \cos 	heta = \frac{5x}{4}$$y = \frac{2(2 \sin 	heta) + 3(4)}{2 + 3} = \frac{4 \sin 	heta + 12}{5} \Rightarrow \sin 	heta = \frac{5y - 12}{4}$Since $\cos^2 	heta + \sin^2 	heta = 1$,we have:$\left(\frac{5x}{4}ight)^2 + \left(\frac{5y - 12}{4}ight)^2 = 1$$\frac{25x^2}{16} + \frac{(5y - 12)^2}{16} = 1$$25x^2 + (5y - 12)^2 = 16$$25x^2 + 25y^2 - 120y + 144 = 16$$25x^2 + 25y^2 - 120y + 128 = 0$This represents the equation of a circle.

Let $A = (0, 4)$ and $B = (2 \cos \theta, 2 \sin \theta)$,for some $0 < \theta < \frac{\pi}{2}$. Let $P$ divide the line segment $AB$ in the ratio $2:3$ internally. The locus of $P$ is

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