The line $L_1$ given by $\dfrac{x}{p} + \dfrac{y}{2} = 1$ passes through the point $(5,0)$. The line $L_2$ given by $\dfrac{x}{10} + \dfrac{y}{q} = 1$ is parallel to $L_1$. Then the distance between the lines $L_1$ and $L_2$ is...

Two lines are given by $x^2 - 4xy + 4y^2 + kx - 2ky = 0$, then the value of k so that the distance between them is 3 is

The line $y = 2x + c$ passes through a point that is equidistant from both the axes and lies in the first quadrant $(x > 0, y > 0)$. Then the value of c is...

If the equation $ax^2 + 4xy - 2y^2 + 4x + 8y + 1 = 0$ represents a pair of straight lines, then the coordinates of their point of intersection are.........