$A$ point moves in the $xy$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $5$ units. The area (in sq units) enclosed by the locus of the point is

The coordinates of the points $A$ and $B$ are $(a, 0)$ and $(-a, 0)$ respectively. If a point $P$ moves such that $PA^2 - PB^2 = 2k^2$,where $k$ is a constant,then the equation to the locus of the point $P$ is:

$A$ variable line $L$ passing through the origin cuts two parallel lines $x-y+10=0$ and $x-y+20=0$ at two points $A$ and $B$ respectively. If $P$ is a point on line $L$ such that $OA, OP, OB$ are in harmonic progression,then the locus of $P$ is

Suppose that the three points $A, B$ and $C$ in the plane are such that their $x$-coordinates as well as $y$-coordinates are in $GP$ with the same common ratio. Then,the points $A, B$ and $C$

If $A=(0,1), B=(1,2), C=(-2,1)$,then the equation of the locus of a point $P(x,y)$ such that the area of triangle $PAB$ equals the area of triangle $PAC$ is:

$A$ line is at a constant distance $c$ from the origin and meets the coordinate axes in $A$ and $B$. The locus of the centre of the circle passing through $O, A, B$ is