Find the angle between the pair of lines repr | vedclass

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(C) The given equation of the pair of straight lines is $x^2+4xy+y^2=0$. Comparing this with the general equation $ax^2+2hxy+by^2=0$,we get $a=1$,$2h=

Vedclass · Accepted Answer

$60$

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(C) The given equation of the pair of straight lines is $x^2+4xy+y^2=0$. Comparing this with the general equation $ax^2+2hxy+by^2=0$,we get $a=1$,$2h=4$ (so $h=2$),and $b=1$. The angle $	heta$ between the pair of lines is given by the formula $	an 	heta = \left| \frac{2\sqrt{h^2-ab}}{a+b} ight|$. Substituting the values,we get $	an 	heta = \left| \frac{2\sqrt{2^2-(1)(1)}}{1+1} ight| = \left| \frac{2\sqrt{4-1}}{2} ight| = \sqrt{3}$. Therefore,$	heta = 	an^{-1}(\sqrt{3}) = 60^{\circ}$.

Find the angle between the pair of lines represented by the equation $x^2+4xy+y^2=0$. (in $^{\circ}$)

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