A moving line intersects the lines $x+y=0$ and $x-y=0$ at the points $A, B$ respectively such that the area of the triangle with vertices $(0,0), A \& B$ has a constant area $C$. The locus of the mid-point $A B$ is given by the equation

A moving line intersects the lines

$x+y=0$ and

$x-y=0$ at the points

$A, B$ respectively such that the area of the triangle with vertices

$(0,0), A \& B$ has a constant area

$C$ . The locus of the mid-point

$A B$ is given by the equation
(A)

$\left(x^{2}+y^{2}\right)^{2}=C^{2}$
(B)

$\left(x^{2}-y^{2}\right)^{2}=C^{2}$
(C)

$(x+y)^{2}=C^{2}$
(D)

$(x-y)^{2}=C^{2}$

Ans(B)

1 Answer

A moving line intersects the lines $x+y=0$ and $x-y=0$ at the points $A, B$ respectively such that the area of the triangle with vertices $(0,0), A \& B$ has a constant area $C$ . The locus of the mid-point $A B$ is given by the equation