The equation of the line passing through $(1, 1)$ and parallel to the line $2x + 3y - 7 = 0$ is

The line passing through the points $(1, 4)$ and $(-5, 1)$ intersects the line $4x + 3y - 5 = 0$ at the point:

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} = $

If a straight line passing through the point $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the $X$-axis and meets the line $12x+5y+10=0$ at $Q$,then the length of $PQ$ 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...

The line $PQ$ with equation $x - y = 2$ intersects the $x$-axis at $P$. Given $Q$ is $(4, 2)$. Find the equation of the line $PQ$ after it is rotated by $45^{\circ}$ in the counter-clockwise direction about point $P$.