Question

Assertion :If the lines represented by $x^2-2mxy-y^2=0$ are rotated about the origin through an angle $\alpha$, one in clockwise direction & other in anticlockwise direction, then equation of bisector of angle between them in new position is given by $m{x}^2+2xy+m{y}^2=0$ Reason: The bisector of the angle between the lines in new position are same as the bisector of the angle between their old positions.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

The Reason (R) is true as the bisector of angle between the lines in new position are same as the bisector of the angle between their old positions,
$\therefore$ The equation of bisectors of the angle of the lines $x^2-2mxy-y^2=0$ is given by $\frac{x^2-y^2}{1-(-1)}=\frac{xy}{-m}$ i.e. $m{x}^2+2xy-m{y}^2=0$
so Assertion (A) is false.
Thus Assertion (A) is false & Reason CR) is true.