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
$16$

Find the value of $a$ :
Given $a x^{2} - y^{2} + 4 x - y = 0$
Comparing the given equation with the general equation
$a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$
We get $a = a, h = 0, b = - 1, g = 2, f = - 1 / 2, c = 0$
$a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0$ represents a pair of straight lines.
$\Rightarrow 0 + 0 - a / 4 + 4 + 0 = 0 \Rightarrow - a / 4 = - 4 \Rightarrow a = 16$
Hence the correct option is B.

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