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The electric potential in a region of space is given by $V (x, y, z) = A (x^{2} - 2 y^{2} + z^{2}),$ Where A is a constant. Then ____

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Locus of equipotential curve in a plane parallel to x-z plane is hyperbola

Locus of equipotential curve in a plane parallel to x-z plane is circle

Locus of equipotential curve in a plane parallel to x-y plane is parabola

Locus of equipotential curve in a plane parallel to x-y plane is hyperbola

answer is B.

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Detailed Solution

Parallel to XZ plane EPS is a circle

$x^{2} + z^{2} = c o n s t$

and parallel to XY plane

$x^{2} - 2 y^{2} = c o n s t$

it is a hyperbola

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