Question

A point moves in the $x-y$ plane such that the sum of its distances from two mutually perpendicular lines is always equal to 3. The area enclosed by the locus of the point is:

• A. $\frac{9}{2}uni{t}^2$
• B. $6uni{t}^2$
• C. $9uni{t}^2$
• D. None of these

Answer 1

Answer: (A)

$\frac{9}{2}uni{t}^2$

From the figure, clearly the equation of the line is
$x+y=3$
So the area enclosed is a traiangle
Area $=\frac{1}{2}\times 3\times 3=\frac{9}{2}squnits$