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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.
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B
Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion.
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C
Assertion is true but Reason is false.
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D
Assertion is false but Reason is true.
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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 $$x^2-2nxy-y^2=0$$

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

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