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  • The least value of , for which the lines <img alt="\mathrm{x=a+m, y=-2}" src="https://entrancecorner.oncod

The least value of |\alpha|, for which the lines \mathrm{x=a+m, y=-2} and \mathrm{y=m x} are concurrent, is

Option: 1

\sqrt{2}


Option: 2

2 \sqrt{2}


Option: 3

0


Option: 4

1


Answers (1)

best_answer

Since lines are concurrent, point of intersection of lines \mathrm{x=\alpha+m} and \mathrm{y=-2} which is \mathrm{(\alpha+m,-2)}  will also satisfy \mathrm{y=m x}

\mathrm{\Rightarrow \mathrm{m}^{2}+\mathrm{ma}+2=0}
Since \mathrm{m} is real \mathrm{\alpha^{2}-8 \geq 0 \Rightarrow|\alpha| \geq 2 \sqrt{2}}.

Hence the least value of \mathrm{|\alpha|=2 \sqrt{2}}.

 

Posted by

Pankaj

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