Question

P is a variable point in the square formed by the lines $x=\pm 1andy=\pm 1$.P moves such. that its distance from the origin is loss than its distance from any side of square. The area traced by the point P is

• A. $\frac{4}{3}\left(4\sqrt{2}+1\right)$
• B. $\frac{4}{3}\left(4\sqrt{2}-1\right)$
• C. $\frac{4}{3}\left(4\sqrt{2}-3\right)$
• D. $\frac{4}{3}\left(4\sqrt{2}-5\right)$

Answer 1

The correct option is C $\frac{4}{3}\left(4\sqrt{2}-3\right)$

$P$ is the variable point in the square formed by the line $x=\pm 1$

$y=\pm 1$

$P$ moves such that is distance from the origin is loss than its distance from any side of square

$\sqrt{x^2+y^2}=\sqrt{1^2+1^2}=\sqrt{2}(1+1{)}^2=(2{)}^2=4$

Hence the volume of the distance $=\frac{4}{3}(4\sqrt{2}-3)$