Question

If the sum of the distances of a moving point from two perpendicular lines in a plane is always $1,$ then, its locus is

• A. Parabola
• B. Ellipse
• C. Hyperbola
• D. None of these

Answer 1

The correct option is D None of these

Suppose that the perpendicular line are drawn as $x-$axis and $y-$axis.
Then sum of distance from the point $P(x,y)$ is $1$
$\therefore |x|+|y|=1$
This would be the locus of the point $P$ which would be a square whose sides are
$x+y=1,-x+y=1,-x-y=1,x-y=1$