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  • If the straight line touches the parabola <img alt="\math

If the straight line \mathrm{y=m x+c(m>0)} touches the parabola \mathrm{y^{2}=8(x+2)}, then the minimum value taken by \mathrm{c} is

Option: 1

12


Option: 2

8


Option: 3

4


Option: 4

6


Answers (1)

best_answer

The tangent of slope \mathrm{m} must be of the form \mathrm{y=m(x+2)+\frac{a}{m}}.

\mathrm{So, 2 m+\frac{2}{m}=c \Rightarrow c=2\left(m+\frac{1}{m}\right) \geq 2 \times 2. So \: \: c_{\min }=4}.

Hence (C) is the correct answer.

 

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Anam Khan

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