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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 $y -$ axis and $z -$ axis is equal to square of its distance from $x z -$ plane, then the locus of point is

x -

axis

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y -

axis

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z -

axis

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x y -

plane

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Solution

The correct option is B $y -$ axis
Let point is $P (x, y, z)$ , then
Distance from $y -$ axis $= \sqrt{x^{2} + z^{2}}$ ,
Distance from $z -$ axis $= \sqrt{y^{2} + x^{2}}$ and
Distance from $x z -$ plane $= | y |$
According to statement,
$(x^{2} + z^{2}) + (y^{2} + x^{2}) = y^{2}$
$\Rightarrow 2 x^{2} + z^{2} = 0$
$\Rightarrow x = 0$ and $z = 0$
$∴$ locus of point is $y -$ axis.

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A point moves such that sum of square of its distances from y− axis and z−axis is equal to square of its distance from xz−plane, then the locus of point is

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