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

Answer 1

The correct option is A A parabola

$(x-h{)}^2+(y-k{)}^2=r^2$
$(x-h{)}^2+(y-k{)}^2=h^2$
$(2-h{)}^2+k^2=h^2$ ........Since, it passes through $(2,0)$]
$k^2=4(h-1)$
$y^2=4(x-1)$ which is a parabola.