Mathematics

if the two pair of lines $2 x ^ { 2 } + 6 x y + y ^ { 2 } = 0$ and $4 x ^ { 2 } + 18 x y + b y ^ { 2 } = 0$ are equally inclined,then $b$ is equal to

$1$

SOLUTION
Given pair of lines are

$2x^2 +6xy+y^2=0$...(1)

and $4x^2+18xy +by^2=0$...(2)

eq. of angle bisector of eq. (1)

$\dfrac {x^2-y^2}{2-1}=\dfrac {xy}{3}$...(3)

eq. of angle bisector of eq. (2)

$\dfrac {x^2-y^2}{2-1}=\dfrac {xy}{9}$...(4)

from eq (3)& (4)

$\dfrac {x^2-y^2}{xy}=\dfrac {1}{3}=\dfrac {4-b}{9}$

$\Rightarrow \dfrac {4-b}{9}=\dfrac {1}{3}$

$\Rightarrow 4-b =3$

$\Rightarrow b=1$

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Single Correct Medium Published on 09th 09, 2020
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