The correct option is C √3y=x+3
Any tangent to y2=4x is of the form y=mx+1m, (∵a=1) and this touches the circle (x−3)2+y2=9.
If ∣∣∣m(3)+1m−0√m2+1∣∣∣=3
[∵ centre of the circle is (3, 0) and radius is 3].
⇒3m2+1m=±3√m2+1
⇒3m2+1=±3m√m2+1
⇒9m4+1+6m2=9m2(m2+1)
⇒3m2=1
⇒m=±1√3
If the tangent touches the parabola and circle above the X-axis, then slope m should be positive.
∴m=1√3 and the equation is y=1√3x+√3
or √3y=x+3.