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 square units) enclosed by the locus of the point is
is​

Answer 1

$\begin{lgathered}\frac{ - 192}{240} = \frac{ - 32}{x} \\ x = \frac{ - 32 \times 240}{ - 192} \\ x = 40\end{lgathered} </p><p>So -192/240 = -32/40$

Answer 2

Step-by-step explanation:

Here, the point moves in the xy-plane such that the sum of its distances from the two mutually perpendicular lines is always equal to 5 units.

∴|x|+|y|=5

⇒x+y=5,x−y=5,−x+y=5,−x−y=5

If we draw these lines on coordinate axis, it will a square of side 52–√(52+52−−−−−−√) units.

∴ Area enclosed = Area of square =(52–√)2=50 square units