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If pairs of straight lines \mathrm{x^2-2 p x y-y^2=0} and \mathrm{x^2-2 q x y-y^2=0} be such that each pair bisects the angle between the other pair, then pq= ?

Option: 1

-1


Option: 2

1


Option: 3

2


Option: 4

-2


Answers (1)

best_answer

According to the question, the equation of the bisectors of the angle between the lines \mathrm{x^2-2 p x y-y^2=0}   .............(1)
is \mathrm{x^2-2 q x y-y^2=0}   .........(2)

\mathrm{\therefore} The equation of bisectors of the angle between the lines (1) is \mathrm{\frac{x^2-y^2}{1-(-1)}=\frac{x y}{-p}}

\mathrm{\Rightarrow-p x^2-2 x y+p y^2=0} .......(3)

since (2) and (3) are identical, comparing (2) and (3), we get \mathrm{\frac{1}{-p}=\frac{-2 q}{-2}=\frac{-1}{p}}

\mathrm{\Rightarrow \quad p q=-1}

Note: By taking the bisectors of the angles between the pair of lines (2), we will get the same result.

Posted by

Divya Prakash Singh

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