Show that if

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.

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now