The joint equation of the pair of lines through the origin and making an angle of $\dfrac{\pi}{4}$ with the line $3x + y - 6 = 0$ is

If a circle with center $(-1, 1)$ touches the line $x + 2y + 4 = 0$, then the co-ordinates of the point of contact are

A point on the parabola $y^2 = \dfrac{36}{5}x$ at which the ordinate increases at thrice the rate of the abscissa is .....

The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 48y$ to the ends of its latus rectum, is .....