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  4. If x2+y2=1, then the point P(x, y, √1-x2-y2) is at a distance of ...A ... units from the origin. Here, A refers to

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Q. If $x^2+y^2=1$, then the point $P\left(x, y, \sqrt{1-x^2-y^2}\right)$ is at a distance of ...A ... units from the origin. Here, A refers to

Introduction to Three Dimensional Geometry

Solution:

The coordinates of point $P$ are $\left(x, y, \sqrt{1-x^2-y^2}\right)$.
Then,
$O P =\sqrt{(x-0)^2+(y-0)^2+\left(\sqrt{1-x^2-y^2}-0\right)^2} $
$ =\sqrt{x^2+y^2+1-x^2-y^2}=\sqrt{1}=1$