Question

Assertion :If the two pair of lines $x^2-2mxy-y^2=0$ and $x^2-2nxy-y^2=0$ are such that one of them represents the bisector of angle between the other, then $1+mn=0$. Reason: Equation of bisector of angle between the pair of lines $a{x}^2+2hxy+b{y}^2=0$ is given by $\frac{x^2-y^2}{a-b}=\frac{xy}{h}.$

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion.
• B. Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion.
• C. Assertion is true but Reason is false.
• D. Assertion is false but Reason is true.

Answer 1

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion.

Given

$x^2-2mxy-y^2=0$

The pair if bisector of given pair is

$\frac{x^2-y^2}{1-(-1)}=\frac{xy}{-m}$

$\frac{x^2-y^2}{2}=\frac{xy}{-m}$ or $x^2+\frac{2xy}{m}-y^2=0$ which

is identical to $x^2-2nxy-y^2=0$

$\therefore \frac{1}{m}=-n\Rightarrow mn+1=0$