(C) The given equation of the pair of straight lines is $ax^2+2hxy+by^2=0$,where $a=1$,$2h=4$ (so $h=2$),and $b=1$. The formula for the angle $\theta$

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(C) The given equation of the pair of straight lines is $ax^2+2hxy+by^2=0$,where $a=1$,$2h=4$ (so $h=2$),and $b=1$. The formula for the angle $\theta$ between the pair of lines is $\tan \theta = \left| \frac{2\sqrt{h^2-ab}}{a+b} \right|$. Substituting the values,we get $\tan \theta = \left| \frac{2\sqrt{2^2-(1)(1)}}{1+1} \right|$. $\tan \theta = \frac{2\sqrt{4-1}}{2} = \sqrt{3}$. Therefore,$\theta = \tan^{-1}(\sqrt{3}) = 60^{\circ}$.

Class 11 Mathematics Pair of straight lines Angle between the pair of straight lines, Condition for parallel and perpendicular lines

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

AP EAMCET 2021 All AP EAMCET

A
$30$
B
$45$
C
$60$
D
$90$

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