If the portion of a line intercepted between the coordinate axes is divided by the point $(2, -1)$ in the ratio $3:2$,then the equation of that line is:

The equation of the line whose midpoint between the axes is $({x_1}, {y_1})$ is:

The number of lines passing through $A(3, 4)$ such that the sum of their non-zero intercepts is zero is:

The Fahrenheit temperature $F$ and absolute temperature $K$ satisfy a linear equation. Given that $K=273$ when $F=32$ and that $K=373$ when $F=212$. Express $K$ in terms of $F$ and find the value of $F$,when $K =0$.

The area of the triangle formed by the line $L$ with the coordinate axes is $12$ sq. units. If $L$ passes through the point $(12, 4)$ and the product $P$ of the $X$-intercept of $L$ and the square of the $Y$-intercept of $L$ is negative,then $P=$

If the straight line passing through the point $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive direction of $X$-axis and meets the line $12x + 5y + 10 = 0$ at $Q$,then the length of $PQ$ is