If the line $\frac{x}{a} + \frac{y}{b} = 1$ passes through the points $(2, -3)$ and $(4, -5)$,then $(a, b) = $

$A$ line $L$ intersects the lines $3x - 2y - 1 = 0$ and $x + 2y + 1 = 0$ at the points $A$ and $B$. If the point $(1, 2)$ bisects the line segment $AB$ and $\frac{x}{a} + \frac{y}{b} = 1$ is the equation of the line $L$,then $a + 2b + 1 = $

Find the equation of a straight line that makes an intercept of $3$ units on the negative direction of the $y$-axis and is inclined at an angle of ${\tan ^{ - 1}}\left( {\frac{3}{5}} \right)$ with the $x$-axis.

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$.

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

Points $A$ and $B$ are in the first quadrant; point $O$ is the origin. If the slope of $OA$ is $1$,the slope of $OB$ is $7$,and $OA = OB = r$,then the slope of $AB$ is: