Let the line $2x + 3y = 18$ intersect the $Y$-axis at $B$. Suppose $C(\neq B)$,with coordinates $(a, b)$,is a point on the line such that $PB = PC$,where $P = (10, 10)$. Then,$8a + 2b$ equals

Suppose that the points $(h, k)$,$(1, 2)$,and $(-3, 4)$ lie on the line $l_1$. If a line $l_2$ passing through the points $(h, k)$ and $(4, 3)$ is perpendicular to $l_1$,then $\left(\frac{k}{h}\right)$ equals

If a line passing through the point $P(1, 1)$ makes an angle $\theta$ with the positive direction of the $x$-axis and intersects the coordinate axes at $A$ and $B$ such that $AB = OP$,where $O$ is the origin,then what is the value of $\tan\theta + \cot\theta$?

If the equation of the base of an equilateral triangle is $2x - y = 1$ and the vertex is $(-1, 2)$,then the length of the side of the triangle is

If a line $ax + 2y = k$ forms a triangle of area $3$ sq. units with the coordinate axes and is perpendicular to the line $2x - 3y + 7 = 0$,then the product of all the possible values of $k$ is

If $L_1$ is a line passing through the point $P(4, -3)$ and perpendicular to the line $3x - 4y + k = 0$,then the distance of $P$ from the line $5x - 3y - 2 = 0$ measured along the line $L_1$ is