If lines represented by equation $p x^{2} - q y^{2} = 0$ are distinct then

p q > 0

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p q < 0

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p q = 0

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p + q = 0

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Solution

The correct option is A $p q > 0$
Given line is $p x^{2} - q y^{2} = 0$
General equation is $a x^{2} + b y^{2} + h = 0$
Comparing above equation with $(i)$ , we get
$a = p, b = - q, h = 0$
Lines are real and distinct if $h^{2} - a b > 0$
$\Rightarrow 0 + p q > 0$
$⟹ p q > 0$

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If lines represented by equation px2−qy2=0 are distinct then

The correct option is A pq>0Given line is px2−qy2=0General equation is ax2+by2+h=0Comparing above equation with (i), we geta=p,b=−q,h=0Lines are real and distinct if h2−ab>0⇒0+pq>0⟹pq>0

If lines represented by equation $p x^{2} - q y^{2} = 0$ are distinct then

The correct option is A $p q > 0$
Given line is $p x^{2} - q y^{2} = 0$
General equation is $a x^{2} + b y^{2} + h = 0$
Comparing above equation with $(i)$ , we get
$a = p, b = - q, h = 0$
Lines are real and distinct if $h^{2} - a b > 0$
$\Rightarrow 0 + p q > 0$
$⟹ p q > 0$