Consider the locus of center of the circle which touches the circle `x^(2)+y^(2)=4` externally and the line x=4. The distance of the vertex of the locus from the otigin is __________ .

Answer

3

Explanation

(3)
The radius of variable circle is 4-h.
It touches `x^(2)+y^(2)=4`. Therefore,
`2+4-h=sqrt(h^(2)+k^(2))`
`or x^(2)+y^(2)=x^(2)-12x+36`
`ory^(2)=-12(x-3)`
The vertex is (3,0).