Question

If the lines represented by $ {{x}^{2}}-2pxy-{{y}^{2}} $ are rotated about the origin through an angle $ \theta $ , one in clockwise direction and other in anti-clockwise direction. Then, die equation of bisectors of the angles between the lines in the new position is

• A. $ p{{x}^{2}}+2xy+p{{y}^{2}}=0 $
• B. $ p{{x}^{2}}-2xy+p{{y}^{2}}=0 $
• C. $ p{{x}^{2}}+2xy-p{{y}^{2}}=0 $
• D. None of these

Answer 1

Answer: (C)

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