(A) The given equation is $3x^{2} + 2xy - y^{2} = 0$. Comparing this with the general form $ax^{2} + 2hxy + by^{2} = 0$,we get $a = 3$,$2h = 2 \implie

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(A) The given equation is $3x^{2} + 2xy - y^{2} = 0$. Comparing this with the general form $ax^{2} + 2hxy + by^{2} = 0$,we get $a = 3$,$2h = 2 \implies h = 1$,and $b = -1$.The joint equation of the pair of angle bisectors is given by the formula $\frac{x^{2} - y^{2}}{a - b} = \frac{xy}{h}$.Substituting the values,we get $\frac{x^{2} - y^{2}}{3 - (-1)} = \frac{xy}{1}$.$\frac{x^{2} - y^{2}}{4} = xy$.$x^{2} - y^{2} = 4xy$.$x^{2} - 4xy - y^{2} = 0$.

Class 11 Mathematics Pair of straight lines Bisectors of the angle between the lines, Point of intersection of the lines

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The joint equation of the bisectors of the angle between the lines represented by $3x^{2} + 2xy - y^{2} = 0$ is:

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A
$x^{2} - 4xy - y^{2} = 0$
B
$x^{2} + 4xy - y^{2} = 0$
C
$x^{2} - 4xy + y^{2} = 0$
D
$x^{2} + 4xy + y^{2} = 0$

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Pair of straight lines

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Bisectors of the angle between the lines, Point of intersection of the lines

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The joint equation of the bisectors of the angle between the lines represented by $3x^{2} + 2xy - y^{2} = 0$ is:

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