The locus of the equation $x^{2} + y^{2} = 0$ is

A circle

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A hyperbola

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A pair of lines

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At the origin

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Solution

The correct option is D
At the origin

Explanation of the correct option.
Compute the locus:
Given : $x^{2} + y^{2} = 0$
It can be written as, $x^{2} = - y^{2}$ .
A perfect square can never be the same as the negative of another perfect square except at $(0, 0)$ .
The loci of the given equation are at the origin.
Hence option $D$ is the correct option.

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