If the point $(5, 2)$ divides the segment of the line between the axes into two equal parts,then its equation is:

The equation of the line,passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \cos \theta - y \sin \theta = a$,is

If $p = a_1 x + b_1 y + k_1 = 0$,$q = a_2 x + b_2 y + k_2 = 0$ and $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{k_1}{k_2}$,then the curve $p + c q = 0$ is

If a line $L$ passes through the point of intersection of the lines $2x + 3y + 1 = 0$ and $x + y - 3 = 0$ and the angle made by the line $L$ with the $X$-axis measured in the positive direction from the positive $X$-axis is $\tan^{-1} \frac{2}{3}$,then the sum of the intercepts made by this line on the axes is

The equation of the line whose slope is $3$ and which cuts off an intercept of $3$ from the positive $x$-axis is

If the slope of a line is $2$ and it makes an intercept of $-4$ on the $y$-axis,then its equation is: