The gradient of the line joining the points on the curve $y = x^2 + 2x$ whose abscissae are $1$ and $3$,is

$PS$ is the median of the triangle with vertices at $P(2, 2)$,$Q(6, -1)$,and $R(7, 3)$. The intercepts on the coordinate axes of the line passing through point $(1, -1)$ and parallel to $PS$ are respectively:

The equation of the line which cuts off an intercept $3$ units on $OX$ and an intercept $-2$ units on $OY$ is:

Find the equation of the line which intersects the $y$-axis at a distance of $2$ units above the origin and makes an angle of $30^{\circ}$ with the positive direction of the $x$-axis.

The equation of the line,passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \cos \theta - y \sin \theta = a$,is

Find the equation of a line perpendicular to the line $x-2y+3=0$ and passing through the point $(1, -2).$