VITEEE 2010 Paper

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