If the sum of distances from a point $P$ to two mutually perpendicular straight lines is $1$ unit, then the locus of $P$ is

If $A=(-1, 2)$ and $B=(1, -2)$ are two points and $P$ is a variable point such that the area of $\triangle PAB$ is always $1$,then the equation of the locus of $P$ is

Find the fixed point through which the line $x(a + 2b) + y(a + 3b) = a + b$ always passes for all values of $a$ and $b$.

$A$ point on the straight line $3x + 5y = 15$ which is equidistant from the coordinate axes will lie only in

Suppose we have to cover the $XY$-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that we can choose tiles of the following shapes: equilateral triangle,square,regular pentagon,regular hexagon. Then,the tiling can be done with tiles of

If a variable line is moving such that the intercepts made by it on the coordinate axes are reciprocal to each other,then the points $P(x, y)$ on such lines satisfy