Question

Let $C$ be a circle and $L$ a line on the same plane such that $C$ and $L$ do not intersect. Let $P$ be a moving point such that the circle drawn with centre at $P$ to touch $L$ also touches $C$. Then the locus of $P$ is -

• A. a straight line parallel to $L$ not intersecting $C$
• B. a circle concentric with $C$
• C. a parabola whose focus is centre of $C$ and whose directrix is $L$.
• D. a parabola whose focus is the centre of $C$ and whose directrix is a straight line parallel to $L$.

Answer 1

Answer: (D)

Correct answer is (d) a parabola whose focus is the centre of $C$ and whose directrix is a straight line parallel to $L$.