Question

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

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.

Solution

## 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 $$\dfrac{x^2-y^2}{1-(-1)}=\dfrac{xy}{-m}$$$$\dfrac{x^2-y^2}{2}=\dfrac{xy}{-m}$$ or $$x^2+\dfrac{2xy}{m}-y^2=0$$ which is identical to $$x^2-2nxy-y^2=0$$$$\therefore \dfrac{1}{m}=-n \Rightarrow mn+1=0$$Maths

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