Question:
Show that if $x^{2}+y^{2}=1$, then the point $\left(x, y \sqrt{1-x^{2}-y^{2}}\right)$ is at a distance 1 unit from the origin.
Solution:
Given $x^{2}+y^{2}=1 \Rightarrow 1-x^{2}-y^{2}=0$
Distance of the point $\left(x, y \sqrt{1-x^{2}-y^{2}}\right)$ from origin is $=$
$\sqrt{x^{2}+y^{2}+\left(\sqrt{1-x^{2}-y^{2}}\right)^{2}}$
$=\sqrt{x^{2}+y^{2}+\left(1-x^{2}-y^{2}\right)}$
$=\sqrt{x^{2}+y^{2}+1-x^{2}-y^{2}}$
$=\sqrt{1}$
$=1$ unit.
When $x=1$ the distance of that point from origin will be 1 unit.