The equation of the common tangent to the curves y2=8x and xy=−1 , is

General equation of tangent to the curve y2=8x is y=mx+2m ------(1) Now on solving it with xy=−1xmx+2m=−1 m2x2+2x+m=0  put discriminant =0 4-4m3=0⇒m=1 sub in(1) y=x+2