Question

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

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

Answer 1

The correct option is C parabola

Let the center of the required circle be C and $C_1$ be $p$ and $P_1$
Draw a line parallel to L at a distance 1 unit from it, where r is the radius of the required circle
Then ${CP}_1=r+1=CM$
$\Rightarrow$ C is equidistant from the point $P_1$ and the line parallel to L
$\Rightarrow$ locus of C is a parabola