(A) The bisectors of the angles between the lines in the new position are the same as the bisectors of the angles between the lines in the original po

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(A) The bisectors of the angles between the lines in the new position are the same as the bisectors of the angles between the lines in the original position.The equation of the pair of bisectors for $ax^2 + 2hxy + by^2 = 0$ is given by $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$.Here,$a = 1$,$h = -p$,and $b = -1$.Substituting these values,we get:$\frac{x^2 - y^2}{1 - (-1)} = \frac{xy}{-p}$$\frac{x^2 - y^2}{2} = \frac{xy}{-p}$$-p(x^2 - y^2) = 2xy$$-px^2 + py^2 = 2xy$$px^2 + 2xy - py^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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If the lines represented by $x^2 - 2pxy - y^2 = 0$ are rotated about the origin by an angle $\theta$ in clockwise and counter-clockwise directions respectively,then the equation of the bisector of the angle between the lines in the new position is:

A
$px^2 + 2xy - py^2 = 0$
B
$px^2 + 2xy + py^2 = 0$
C
$x^2 - 2pxy + y^2 = 0$
D
None of these

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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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If the lines represented by $x^2 - 2pxy - y^2 = 0$ are rotated about the origin by an angle $\theta$ in clockwise and counter-clockwise directions respectively,then the equation of the bisector of the angle between the lines in the new position is:

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