List of top Mathematics Questions on Various Forms of the Equation of a Line asked in KEAM

Let $O$ be the origin and $P$ be a point on a line such that $OP$ is perpendicular to that line. If $OP$ makes an obtuse angle $\alpha$ with the $x$-axis, $OP = 5$ and $\sin \alpha = \frac{3}{5}$, then the equation of the line is

Let O be the origin and let P be a point on the line \(x + \sqrt{3}y = 10\). If OP is perpendicular to the line, then the angle between OP and the y-axis is

If $a y = x + b$ is the equation of the line passing through the points (-5, -2) and (4, 7), then the value of $2a + b$ is equal to:

Which one of the following lines passes through the point of intersection of $x+y=5$ and $2x+y=7$? ________.