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If the lines represented by \mathrm{x^2-2 p x y-y^2=0} are rotated about the origin through an angle \mathrm{\theta}, one in clockwise direction and other in anti-clockwise direction, find the equation of the bisectors of the angle between the lines in the new position.

Option: 1

\mathrm{p x^2-2 x y+p y^2=0}


Option: 2

\mathrm{-p x^2-2 x y+p y^2=0}


Option: 3

\mathrm{p x^2-2 x y-p y^2=0}


Option: 4

None of these.


Answers (1)

best_answer

The bisectors of the angles between the lines in new position are same as the bisectors of the angles between their old positions. Therefore, the required equation is \mathrm{\frac{x^2-y^2}{1-(-1)}=\frac{x y}{-p} \Rightarrow p x^2+2 x y-p y^2=0}.

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shivangi.shekhar

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