Solving the given equations, (mx+c)2=4ax−a3 ⇒m2x2+2mc.x+c2=m4ax−4a3 ⇒m2x2+(2mc−4a)x+c2+4a3=0 Since the straight line touches the parabola at a point, so, the discriminant =0 ⇒(2mc−4a)2−4m2(c2+4a3)=0 ⇒4m2c2−16amc+16a2−4m2c2−16a3m2=0 ⇒−mc+a−a2m2=0 ⇒mc=a−a2m2⇒c=