Let the centre of circle is (b, and radius of circle is k Center of another circle (0, 3) and radius is 2 Both circles touch each other ∴√(h−0)2+(k−3)2=k+2 ⇒√h2+k2−6k+9=k+2 ⇒h2+k2−6k+9=k2+4k+4 ⇒h2=10k−5 ⇒x=10y−5 which represent equation of parabola ∴ Locus of centre of circle is parabola.