The line $2x+y=4$ intersects X and Y axes at points A and B respectively. Let $C(p, q)$ be the point such that the lines AC and BC are perpendicular. The distance of point C from the midpoint of segment AB is...

If the distance between the lines represented by $(x - 2y)^2 + k(x - 2y) = 0$ is $3$ units and $k > 0$ then the equations of the lines are

If the slope of one of the two lines given by $\dfrac{x^2}{a} + \dfrac{2xy}{h} + \dfrac{y^2}{b} = 0$ is twice that of the other, then $h^2 : ab = $ ...

If the equation $3x^2 + (3 - p)xy + qy^2 - 2px = 8pq$ represents a circle, then the area (in sq. units) of this circle is