The equation of a line is $3x - 4y + 10 = 0$. Find its $x$-intercept and $y$-intercept.

The parallelism condition for two straight lines,one of which is specified by the equation $ax + by + c = 0$ and the other being represented parametrically by $x = \alpha t + \beta$ and $y = \gamma t + \delta$,is given by:

The equation of the line passing through the point $(1, 2)$ and perpendicular to the line $x + y + 1 = 0$ is

$A$ man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $\frac{1}{4}$. Three stones $A, B$ and $C$ are placed at the points $(1,1), (2,2)$ and $(4,4)$ respectively. Which of these stones is/are on the path of the man?

Find the equation of the line such that the perpendicular drawn from the origin to the line makes an angle of $30^{\circ}$ with the $x$-axis and the line forms a triangle of area $\frac{50}{\sqrt{3}}$ with the axes.

The vertex $A$ of a triangle lies on the lines $x+y=1$ and $2x+3y=6$. If the orthocentre of the triangle is $O\left(\frac{3}{7}, \frac{22}{7}\right)$,then the equation of $OA$ in the normal form is