Let P be a variable point on a circle C and Q | vedclass

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(A) Let the circle $C$ have center $O(x_0, y_0)$ and radius $r$. The coordinates of any point $P$ on the circle can be represented as $P(x_0 + r \cos

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(A) Let the circle $C$ have center $O(x_0, y_0)$ and radius $r$. The coordinates of any point $P$ on the circle can be represented as $P(x_0 + r \cos 	heta, y_0 + r \sin 	heta)$.Let $Q$ be the fixed point $(a, b)$.Let $R(h, k)$ be the midpoint of the line segment $PQ$.Then, $h = \frac{x_0 + r \cos 	heta + a}{2}$ and $k = \frac{y_0 + r \sin 	heta + b}{2}$.Rearranging these equations, we get:$2h - (x_0 + a) = r \cos 	heta$$2k - (y_0 + b) = r \sin 	heta$Squaring and adding both equations:$(2h - (x_0 + a))^2 + (2k - (y_0 + b))^2 = r^2(\cos^2 	heta + \sin^2 	heta)$$4(h - \frac{x_0 + a}{2})^2 + 4(k - \frac{y_0 + b}{2})^2 = r^2$$(h - \frac{x_0 + a}{2})^2 + (k - \frac{y_0 + b}{2})^2 = (\frac{r}{2})^2$This is the equation of a circle with center $(\frac{x_0 + a}{2}, \frac{y_0 + b}{2})$ and radius $\frac{r}{2}$.

Let $P$ be a variable point on a circle $C$ and $Q$ be a fixed point outside $C$. If $R$ is the midpoint of the line segment $PQ$, then the locus of $R$ is

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