The area (in square units) of the quadrilateral formed by the point of intersection of the lines $x+y-1=0$, $x-y+1=0$, the point $(1,1)$ and the feet of the perpendiculars from this point on to the lines is

The condition that the lines joining the origin to the points of intersection of the two curves $x^2+y^2+g x+c=0, x^2+y^2+2 f y-c=0$ are at right angles, is

If $\alpha$ represent the square of the distance between the origin and the point of intersection of the lines $x^2-y^2-x+3 y-2=0$ and $\beta$ represent the product of the perpendicular distances from the origin on the pair of lines, then $\alpha \beta=$

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