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If lines represented by equation $p x^{2}-q y^{2}=0$ are distinct then (A) $p q>0$ (B) $p q
If lines represented by equation $p x^{2}-q y^{2}=0$ are distinct then
(A) $p q>0$
(B) $p q<0$
(C) $p q=0$
(D) $p+q=0$
maths | Maths
If lines represented by equation $p x^{2}-q y^{2}=0$ are distinct then
(A) $p q>0$
(B) $p q<0$
(C) $p q=0$
(D) $p+q=0$

Correct option is

(A) $\mathrm{pq}>0$

Given line is $\mathrm{px}^{2}-\mathrm{qy}^{2}=0$

General equation is $a x^{2}+b y^{2}+h=0$

Comparing above equation with (i), we get $\mathrm{a}=\mathrm{p}, \mathrm{b}=-\mathrm{q}, \mathrm{h}=0$

Lines are real and distinct if $\mathrm{h}^{2}-\mathrm{ab}>0$

$

\begin{array}{l}

\Rightarrow 0+\mathrm{pq}>0 \\

\Longrightarrow \mathrm{pq}>0

\end{array}

$

i

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