The curve $y^{2} (a^{2} + x^{2}) = x^{2} (a^{2} - x^{2})$ is symmetric about

x -

axis

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y -

axis

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straight line

x = y

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Origin

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Solution

The correct option is D Origin
We have,
$y^{2} (a^{2} + x^{2}) = x^{2} (a^{2} - x^{2})$
$\Rightarrow f (x, - y) = f (x, y)$
$∴$ Symmetric about $x -$ axis
$f (- x, y) = f (x, y)$
$∴$ Symmetric about $y -$ axis
$f (- x, - y) = f (x, y)$
$∴$ Symmetric about origin
$f (x, y) \neq f (y, x)$
$∴$ Not Symmetric about $y = x$ line

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