A) 8
B) 16
C) 24
D) 32
Correct Answer: C
Solution :
The equation of any normal to the parabola \[{{y}^{2}}=-8x\,\,\text{is}\,\,y=mx+4m+2{{m}^{3}}\] ?(i) (using equation of normal of parabola in slope form \[y=mx-2am-a{{m}^{3}}\]and \[a=-2\]) But, the given normal is \[2x+y+k=0\] \[\Rightarrow \] \[y=-2x-k\] ?(ii) Comparing Eqs. (i) and (ii), we get \[m=-2\] and \[-\,4m-2{{m}^{3}}=k\] \[\Rightarrow \] \[k=8+16=24\]
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