Consider the locus of centre of circle which touches circle x2+y2=4 and line x=4 . The distance of the vertex of
the locus from origin is
Radius of variable circle is 4−h .
It touches x2+y2=4
Then 2+4−h=h2+k2 or x2+y2=x2−12x+36
⇒ y2=−12(x−3) The vertex (3,0) .