Question

A point moves in the $xy$ -plane such that the sum of its distance from two mutually perpendicular lines is always equal to 5 units. The area (in sq units) enclosed by the locus of the point, is

• A. $\frac{25}{4}$
• B. 25
• C. 50
• D. 100

Answer 1

Answer: (C)

In a figure, $x{x}^{\prime }$ and $y{y}^{\prime }$ are two perpendicular axes.
$\therefore |x|+|y|=5$
$\therefore$ Coordinates of $B$ and $C$ are $(5,0)$ and $(0,5)$
$\therefore$ Length of $BC=\sqrt{5^2+5^2}=5\sqrt{2}$
$\therefore$ Area of square $ABCD=(5\sqrt{2}{)}^2=50$