Question

A variable circle passes through the fixed point (2,0) and touches the y-axis . Then the locus of its centre is

• A. A circle
• B. An Ellipse
• C. A hyperbola
• D. A parabola

Answer 1

The correct option is D A parabola

Suppose the centre of circle be (h,k).
Since it touches the y-axis, $\therefore$ radius of circle = h

Now $(h-2{)}^2+k^2=h^2\Rightarrow h^2+4-4h+k^2=h^2$
$\Rightarrow k^2$ = 4 h - 4. Hence the locus of centre is $y^2$= 4x - 4, which is a parabola.