If the pair of lines $x^2-16 p x y-y^2=0$ and $x^2-16 q x y-$ $y^2=0$ are such that each pair bisects the angle between the other pair, then $\mathrm{pq}=$

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Aicharya · Accepted Answer

We have, equations of pair of straight lines

Now, equations of bisectors of these line are $ -8 p x^2-2 x y+8 p y^2=0 $

and $-8 q x^2-2 x y+8 q y^2=0$

According to the given condition in the data, Eqs. (i) and (iv), and Eqs. (ii) and (iii) must be coincident. So, $ \begin{gathered} \frac{1}{4 q}=\frac{-16 p}{1}=\frac{-1}{-4 q} \\ 1=-64 p q \\ \therefore \quad p q=\frac{-1}{64} \end{gathered} $

If the pair of lines $x^2-16 p x y-y^2=0$ and $x^2-16 q x y-$ $y^2=0$ are such that each pair bisects the…

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