Question

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

Answer 1

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

Now (h−2)2+k2=h2⇒h2+4−4h+k2=h2
⇒ k2 = 4 h - 4. Hence the locus of centre is y2= 4x - 4, which is a parabola.