If the circle `(x-6)^(2)+y^(2)=r^(2)` and the parabola `y^(2)=4x` have maximum number of common chords, then the least integral value of r is __________ .

Answer

5

Explanation

(5) For maximum number of common chords, the circle and the parabola must intersect at four distinct points.
Let us first find the of r when circle and the parabola touch each other.
For that, solving the given curves, we have
`(x-6)^(2)+4x=r^(2)`
`orx^(2)-8x+36-r^(2)=0`
The curves touch if discriminant
`D=64-4(36-r^(2))=0`
`orr^(2)=20`
Hence, the least integral value of r for which the curves intersect is 5.