The equation of the line passing through the origin and the point $(a \cos \theta, a \sin \theta)$ is .....

Find the value of $k$ for which the line $(k-3)x - (4-k^2)y + k^2 - 7k + 6 = 0$ is parallel to the $x$-axis.

If the line $y = mx + c$ passes through the points $(2, 4)$ and $(3, -5)$,then:

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?

Find the slope of the line making an inclination of $60^{\circ}$ with the positive direction of the $x$-axis.

Let $\alpha \in R$. If the line $(\alpha+1) x+\alpha y+\alpha=1$ passes through a fixed point $(h, k)$ for all $\alpha$,then $h^2+k^2=$