Since, the equation of tangent to parabola y2=4x is y=mx+
1
m
. . . . (i) The line (i) is also the tangent to circle x2+y2−6x=0 Then centre of circle =(3,0) radius of circle =3 The perpendicular distance from centre to tangent is equal to the radius of circle ∴
|3m+
1
m
|
√1+m2
=3⇒(3m+
1
m
)2=9(1+m2) ⇒m=±
1
√3
Then, from equation (i): y=±
1
√3
x±√3 Hence, √3y=x+3 is one of the required common tangent.