If the line kx+y=4 touches the parabolay=x−x2 then the point of contact is

4−kx=x−x2 or x2−(k+1)x+4=0 has coincidentroots if (k+1)2−16=0⇒k=3 or −5So x=±2a and the points of contact are (2, – 2)or (– 2, – 6).