Let $P$ be a variable point on a circle $C$ and $Q$ be a fixed point outside $C$. If $R$ is the mid-point of the line segment $P Q$, then the locus of $R$ is (a) a circle (b) an ellipse (c) a line segment (d) segment of a parabola.
(a) Compute for $C = \left\{ x ^ { 2 } + y ^ { 2 } = 1 \right\}$ and $Q = ( a , 0 )$ for some $a > 1$.
Let $P$ be a variable point on a circle $C$ and $Q$ be a fixed point outside $C$. If $R$ is the mid-point of the line segment $P Q$, then the locus of $R$ is\\
(a) a circle\\
(b) an ellipse\\
(c) a line segment\\
(d) segment of a parabola.