Question

A cat wants to catch a rat. The cat follows the path whose equation is x + y = 0, but the rat follows the path whose equation is$x^2+y^2=4$. The coordinates of possible points of catching the rat are?

• A. $(2,2)$
• B. $(\sqrt{2},-\sqrt{2})$
• C. $(2,3)$
• D. $(0,0)$

Answer 1

Answer: (B)

$(\sqrt{2},-\sqrt{2})$

Here,

The cat can catch the rat only if both their trajectories meet.

Let the meeting point be $(x,y)$

$x+y=0,x^2+y^2=4$

Both should satisfy the point.

Substituting, $x=-y$

2x^2=4$

$x=\pm \sqrt{2}=-y$

The points can be,

$(\pm \sqrt{2},\mp \sqrt{2})$

The only option is $B$

Option $\text{B}$ is the correct answer