IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

Discussion Response Post to: pair of straight lines

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27 Apr 2008 14:56:45 IST

Subject: Re:pair of straight lines

srujana (3220)

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$sagarvaze\;is\;right,$

$If\;the\;equation\;ax^2+2hxy+by^2+2gx+2fy+c=0\;represents\;two\;straight\;lines,$

$the\ angle\ between\ the\ pair\ of\ straight\ lines\ \theta\;is\;given\;by,$

$\theta=tan^{-1}(\frac{2\sqrt{h^2-ab}}{a+b})$

$\Rightarrow\;tan\theta=\frac{2\sqrt{h^2-ab}}{a+b}$

$If\ the\ lines\ are\ parallel,\ then\ tan\theta=0$

$\Rightarrow\sqrt{h^2-ab}=0$

$\Rightarrow h^2=ab\;\$

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