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Pair of Straight Lines

If a x 2 - ...

Question

If $a x^{2} - y^{2} + 4 x - y = 0$ represents a pair of lines, then $a$ is equal to:

- 16

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16

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4

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- 4

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Solution

The correct option is B $16$
The equation $a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$ represents a pair of straight lines if $a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0$
Here, $a = a, b = - 1, h = 0, g = 2, f = \frac{- 1}{2}, c = 0$
$\Rightarrow 0 + 0 - \frac{a}{4} + 4 - 0 = 0$
$\Rightarrow a = 16$

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