Question

P is the variable point in the square formed by the the lines $x=\perp +1$ and $y=\perp 1$,P moves such that its distance from the origin is less than its distance from any side of the 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. $\frac{4}{3}(4\sqrt{2\_5}$

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 lines $x=\perp +1$ and $y=\perp 1,P$ moves such that its distance from the origin is less than its distance from any side of the square.

The area traced by the point $P$ is:-

$=\frac{1}{2}\times \sqrt{x^2-y^2}\times \frac{8}{3}$

$=\frac{4}{3}\left(4\sqrt{2-3}\right)$ .