Question

If the lines represented by $x^2-2pxy-y^2$ are rotated about the origin through an angles, one in clockwise direction and other in and-clockwise direction. Then, the 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 the above

Answer 1

Answer: (C)

$p{x}^2+2xy-p{y}^2=0$

The bisectors of the angles between the lines in the new position are same as the bisectors of the angles between their old position.

Therefore, required equation is
$\frac{x^2-y^2}{1-(-1)}=\frac{xy}{-p}$
$\Rightarrow -p{x}^2+p{y}^2=2xy$
$\Rightarrow p{x}^2+2xy-p{y}^2=0$

Hence, option C is correct.