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Byju's Answer

Standard IX

Mathematics

Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

The combined ...

Question

The combined equation of the lines $l_{1}, l_{2}$ is $2 x^{2} + 6 x y + y^{2} = 0$ and that of the lines $m_{1}, m_{2}$ is $4 x^{2} + 18 x y + y^{2} = 0$ . If the angle between $l_{1}$ and $m_{2}$ be $α$ then the angle between $l_{2}$ and $m_{1}$ will be

\frac{π}{2} - α

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2 α

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\frac{π}{4} + α

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α

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Solution

The correct option is D $α$
The combined equation of bisector angles between the lines of the first pair is
$\frac{x_{2} - y_{2}}{a - b} = \frac{x y}{h}$
so, $\frac{x^{2} - y^{2}}{2 - 1} = \frac{x y}{3}$ ------------(1)
and that of other pair is
$\frac{x^{2} - y^{2}}{4 - 1} = \frac{x y}{9}$ -------------(2)
As these equations are the same,
Therefore the two pairs are equally inclined to each other

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The combined equation of the lines l1,l2 is 2x2+6xy+y2=0 and that of the lines m1,m2 is 4x2+18xy+y2=0. If the angle between l1 and m2 be α then the angle between l2 and m1 will be

The combined equation of the lines $l_{1}, l_{2}$ is $2 x^{2} + 6 x y + y^{2} = 0$ and that of the lines $m_{1}, m_{2}$ is $4 x^{2} + 18 x y + y^{2} = 0$ . If the angle between $l_{1}$ and $m_{2}$ be $α$ then the angle between $l_{2}$ and $m_{1}$ will be