The equation of the common tangent touching the  circle (x−3)2+y2=9 and the parabola y2=4x above the x- axis is

The equation of tangent to the given parabola having slope m is y=mx+1m----(1) The equation of tangent to the given circle having slope m is y=m(x−3)±31+m2---(2)Equations ( 1) and (2) are identical. So,    1m=−3m±31+m2 or     1+3m2=±3m1+m2 or     1+6m2+9m4=9m2+m4 or      3m2=1 or      m=±13 Hence, the equation of common tangent is 3y=x+3(as tangent is lying above the x-axis).