The equation of the straight line passing through $(-a, 0)$ and forming a triangle with the coordinate axes of area $T$ is

The owner of a milk store finds that he can sell $980$ liters of milk each week at Rs $14$ per liter and $1220$ liters of milk each week at Rs $16$ per liter. Assuming a linear relationship between selling price and demand,how many liters could he sell weekly at Rs $17$ per liter?

Three points $P(h, k)$,$Q(x_{1}, y_{1})$ and $R(x_{2}, y_{2})$ lie on a line. Show that $(h-x_{1})(y_{2}-y_{1}) = (k-y_{1})(x_{2}-x_{1})$.

$A$ line passes through $P(-4, 1)$ and meets the coordinate axes at points $A$ and $B$. If $P$ divides the segment $AB$ internally in the ratio $1:2$,then the equation of the line is

If the normal form of the equation of a straight line $4x + 3y + 2 = 0$ is $x \cos \alpha + y \sin \alpha = p$ and its intercept form is $\frac{x}{a} + \frac{y}{b} = 1$,then $\frac{p \sec \alpha}{ab} = $

$A$ straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60^o$ with the line $x + y = 0$. Then an equation of the line $L$ is