If the lines represented by $a x^2-b x y-y^2=0$ make angle $\alpha$ and $\beta$ with the positive direction of $X$-axis, then $ an (\alpha+\beta)=$

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If the lines represented by $a x^2-b x y-y^2=0$ make angle $\alpha$ and $\beta$ with the positive direction of $X$-axis, then $	an (\alpha+\beta)=$

Aicharya · Accepted Answer

$	an \alpha$ and $	an \beta$ are roots of the $a x^2-b x y-y^2=0$ $\begin{aligned} & 	herefore 	an \alpha+	an \beta=\frac{-(-\mathrm{b})}{-1}=-\mathrm{b} 	ext { and } 	an \alpha 	an \beta=\frac{\mathrm{a}}{(-1)}=-\mathrm{a} \ & 	an (\alpha+\beta)=\frac{	an \alpha+	an \beta}{1-	an \alpha 	an \beta}=\frac{-\mathrm{b}}{1-(-\mathrm{a})}=\frac{-\mathrm{b}}{1+\mathrm{a}} \end{aligned}$

If the lines represented by $a x^2-b x y-y^2=0$ make angle $\alpha$ and $\beta$ with the positive direction…

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