Question

A point moves in the $x y$ -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 $B C=\sqrt{5^{2}+5^{2}}=5 \sqrt{2}$
$\therefore $ Area of square $A B C D=(5 \sqrt{2})^{2}=50$