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The straight-line \mathrm{y=\mu x+\lambda,(\mu>0)} touches the parabola \mathrm{y^2=16(x+4)}, then the minimum value taken by \mathrm{' \lambda '} is.
 

Option: 1

4


Option: 2

8


Option: 3

16


Option: 4

32


Answers (1)

best_answer

Tangent to \mathrm{y^2=16(x+4)} is

\mathrm{y=\mu(\mathrm{x}+4)+\frac{4}{\mu} }

\mathrm{\therefore \lambda=4 \mu+\frac{4}{\mu} \Rightarrow \lambda \geq 8 }
Hence, the minimum value of \mathrm{\lambda\: is \: 8}

Hence option 2 is correct.

Posted by

Gautam harsolia

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