The line which is parallel to x-axis and crosses the curve y=x at an angle of 45∘, is

The equation of a line parallel to x-axis is y=k.Solving this equation with y=x, we get x=k2.Thus, the line y=k intersect with y=x at k2, k.It is given that the line y=k intersects the curve y=x at an angleor n/4.This means that the slope of the tangent to y=x atk2, k is tan⁡(±π/4)=±1.⇒dydxk2, k=±1⇒12xk2, k=±1⇒k=±12Hence, the required lines are y=±12