The equation of any normal to the parabola y2=−8xisy=mx+4m+2m3...(i) (using equation of normal of parabola in slope form y=mx−2am−am3anda=−2 ) The given normal is 2x + y + k = 0 ⇒ y = -2x - k...(ii) Comparing eqs. (i) and (ii), we get m=−2and−4m−2m3=k ⇒ k=8+16=24