Question

A circle touches the line and the circle $C_1$ externally such that both the circles are on the same side of the line. The locus of the centre of the circle is

• A. part of straight line
• B. parabola
• C. ellipse
• D. hyperbola

Answer 1

The correct option is D hyperbola

Let $C_2$ represent new circle of radius $r$.
$C_1$ and $l$ be given circle of radius $R$ and line.
The perpendicular distance of $C_2$ centre from line is $r$ and distance from $C_1$ centre is $(R+r)$.
If $l$ is directrix and $C_1$ centre is focus, then eccentricity, $e=\frac{R+r}{r}>1$
So, the locus of new circle is hyperbola.