Question

A point moves in the $xy-$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. $18sq$. units
• B. $15sq$. units
• C. $9sq$. units
• D. $27sq$. units

Answer 1

The correct option is A $18sq$. units

Let us assume that mutually perpendicular axis x and y are axis of the cartesians co-ordinate.

$\therefore x+y=3$

A straight line does not have any area enclosed.

But the area with perpendicular axis is a right angled triangle with base $3$ and height $3$.

$\therefore Area=\frac{3\times 3}{2}=4.5sq.units$

Since, locus exists in all $4$ quadrants of the areas

$\therefore 4.5\times 4=18sq.units$