Determine the nature of line represented by $p x^{2} - q y^{2} = 0$ .

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Solution

$p x^{2} - q y^{2} = 0 \Rightarrow {(\sqrt{p x})}^{2} - {(\sqrt{q y})}^{2} = 0 \Rightarrow (\sqrt{p x} - \sqrt{q y}) (\sqrt{p x} + \sqrt{q y}) = 0 \Rightarrow \sqrt{p x} - \sqrt{q y} = 0 a n d \sqrt{p x} + \sqrt{q y} = 0$

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