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Equation of Circle with (h,k) as Center

A point moves...

Question

A point moves such that sum of square of its distances from $x -$ axis and $y -$ axis is equal to square of its distance from $z -$ axis, then the locus of point is

X -

axis

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Z -

axis

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X Y -

plane

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Y Z -

plane

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Solution

The correct option is C $X Y -$ plane
Let point is $P (x, y, z)$ , then
Distance from $x -$ axis $= \sqrt{y^{2} + z^{2}}$ ,
Distance from $y -$ axis $= \sqrt{x^{2} + z^{2}}$ ,
Distance from $z -$ axis $= \sqrt{y^{2} + x^{2}}$
According to statement,
$(y^{2} + z^{2}) + (x^{2} + z^{2}) = y^{2} + x^{2} \Rightarrow z^{2} = 0 ∴ z = 0$
$i . e . X Y -$ plane

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