The equation $16 x^{4} - y^{4} = 0$ represents a:

Point

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Hyperbola

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Pair of straight lines

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Straight line

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Solution

The correct option is C Pair of straight lines
Given equation is $16 x^{4} - y^{2} = 0$
$\Rightarrow (4 x^{2} - y^{2}) (4 x^{2} + y^{2}) = 0$
$\Rightarrow (2 x - y) (2 x + y) (4 x^{2} + y^{2}) = 0$
Since both $x$ and $y$ are real, hence
$4 x^{2} + y^{2} = 0$ can only be zero, if $(x, y) = 0$ .
Thus $4 x^{2} + y^{2} = 0$ represents a point.
And $(2 x - y) (2 x + y) = 0$ $\Rightarrow 2 x - y = 0$ or $2 x + y = 0$ .
Thus, it represents a pair of straight lines.

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