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If three distinct and real normals can be drawn to \mathrm{y^2=8 x} from the point \mathrm{(a, 0)} then
 

Option: 1

\mathrm{a>2}


 


Option: 2

\mathrm{a>4}
 


Option: 3

\mathrm{a} \in(2,4)
 


Option: 4

\text{None of these}


Answers (1)

best_answer

Equation of normal in terms of \mathrm{m} is \mathrm{y=m x-4 m-2 m^3}. If it passes through \mathrm{(a, 0)} then \mathrm{a m-4 m-2 m^3=0}

\mathrm{\Rightarrow \quad \mathrm{m}\left(\mathrm{a}-4-2 \mathrm{~m}^2\right)=0 \quad \Rightarrow \mathrm{m}=0, \mathrm{~m}^2=\frac{\mathrm{a}-4}{2}.}

For three distinct normal, \mathrm{a-4>0 \Rightarrow a>4}

Hence option 2 is correct.

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chirag

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