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 at C
• B. a circle concentric with C
• C. a parabola whose focus is center of C and whose directrix is L
• D. a parabola whose focus is the center of C and whose directrix is a straight line parallel to L

Answer 1

The correct option is D a parabola whose focus is the center of C and whose directrix is a straight line parallel to L

A locus is a set of points satisfying a given condition

The parabola is defined as the locus of a point which moves so that it is always the same distance from a fixed point (called the focus) and a given line (called the directrix).

From the question the moving point is the point $P$ and the fixed line is the directrix,and $P$ is the focus.

Thus the locus of $P$ is a parabola whose focus is the center $C$ and whose directrix is a straight line parallel to $L$