An equation of a common tangent to the parabolay2=4x and x2=4y is

Equation of a tangent to y2=4x is y=mx+1/mIf it touches the parabola x2=4y then the roots ofthe equation x2=4(mx+1/m) are coincident. So(4m)2+16m=0⇒m=−1 and the equation ofthe tangent is x + y + 1 = 0.