The equation $(x^{2} - a^{2})^{2} + (y^{2} - b^{2})^{2} = 0$ represent points which are

collinear

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on a circle centre

(a, b)

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on a circle centre

(0, 0)

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coincident

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Solution

The correct option is C on a circle centre $(0, 0)$
$(x^{2} - a^{2})^{2} + (y^{2} - b^{2})^{2} = 0$ represents points
$x =_{-}^{+} a$ and $y =_{-}^{+} b$
$∴ (a, b), (a, - b), (- a, b)$ and $(- a, - b)$ are four points
These point lie on a circle whose centre is at $(0, 0)$ and radius is $\sqrt{a^{2} + b^{2}}$

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