The equation of the common tangents to the circle`(x-3)^(2)+y^(2)=9` and the parabola `y^(2)=4ax` the x-axis, is

Options

A. `sqrt2y=3x+1`
B. `sqrt3y=-(x+3)`
C. `sqrt3y=x+3`
D. `sqrt3y=-(3x+1)`

Answer

C

Explanation

Let the common tangent to the parabola
`y^(2)=4xbe,`
`y=mx+1/m`
It should be also touch the circle
`(x-3)^(2)+y^(2)=9`
Whose centre is (3,0) and radius =3, then
`(|em+1//m|)/(sqrt(1+m^(2)))=3`
`implies3m^(2)=1`
`impliesm=pm(1)/(sqrt3)`
But `m gt 0,` then equatio of common tangent is
`y=(1)/(sqrt3)*x+sqrt3`
`or sqrt3*y=x+3`