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  • If    is a normal to the parabola <img alt="\mathrm{y^

If  \mathrm{2 x+y+k=0}  is a normal to the parabola \mathrm{y^2=-8 x} , then the value of \mathrm{k} is 

Option: 1

-16


Option: 2

-8


Option: 3

-24


Option: 4

24


Answers (1)

best_answer

The equation of any normal to \mathrm{y^2=-8 x} is

\mathrm{y=m x+4 m+2 m^2 }\quad \dots(i)\quad \quad\mathrm{[Using \left.y=m x-2 a m-a m^3\right] }
 The given line is \mathrm{2 x+y+k=0 } is

\mathrm{y=-2 x-k} \quad \quad \dots(ii)
Comparing (i) and (ii), we get \mathrm{m=-2} and \mathrm{k=-4 m-2 m^3} \mathrm{\Rightarrow k=8+16=24.}

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vinayak

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