AIEEE 2005 Math Solved Paper

Equation of circle with center (0,3) and radius 2 is
x2+(y−3)2=4
Let locus of the variable circle is (α,β)
As it touches x-axis.
∴ It's equation is (x−α)2+(y+β)2=β2Circle touch externally ⇒c1c2=r1+r2
‌∴√α2+(β−3)2=2+β
‌α2+(β−3)2=β2+4+4β
‌⇒α2=10(β−1∕2)
∴ Locus is x2=10(y−‌

1

2

) which is parabola.