If the lines represented by x^2 - 2pxy - y^2 | vedclass

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Question

(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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$px^2 + 2xy - py^2 = 0$

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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$

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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