Write the equation of the line passing through the points $(1, -1)$ and $(3, 5)$.

The $x$-intercept and $y$-intercept of the line $2x - 3y = 6$ are respectively:

The equation of the line which cuts off the intercepts $2a \sec \theta$ and $2a \csc \theta$ on the axes is

If a line $L$ passing through the point $A(-2, 4)$ makes an angle of $60^{\circ}$ with the positive direction of $X$-axis in the anti-clockwise direction and $B(p, q)$ lying in the $3^{\text{rd}}$ quadrant is a point on $L$ at a distance of $6$ units from the point $A$,then $\sqrt{p^2+q^2-8q} = $

The equation of the line,which bisects the line segment joining the points $(2, -19)$ and $(6, 1)$ and is perpendicular to the line joining the points $(-1, 3)$ and $(5, -1)$,is

Find the value of $k$ for which the line $(k-3) x - (4-k^2) y + k^2 - 7k + 6 = 0$ is parallel to the $y$-axis.