If $A$ and $B$ are two points on the line $3x + 4y + 15 = 0$ such that $OA = OB = 9$ units, then the area of the triangle $OAB$ is

Let $PS$ be the median of the triangle with vertices $P(2,2) , Q(6,-1) $ and $R(7,3) $. The equation of the line passing through $(1,-1) $ and parallel to $PS $ is :

The equation of base $BC$ of an equilateral triangle is $3x + 4y = 1$ and vertex is $(-3,2),$ then the area of triangle is-

Show that the path of a moving point such that its distances from two lines $3 x-2 y=5$ and $3 x+2 y=5$ are equal is a straight line.

If in a parallelogram $ABDC$, the coordinates of $A, B$ and $C$ are respectively $(1, 2), (3, 4)$ and $(2, 5)$, then the equation of the diagonal $AD$ is

For a point $P$ in the plane, let $d_1(P)$ and $d_2(P)$ be the distance of the point $P$ from the lines $x-y=0$ and $x+y=0$ respectively. The area of the region $R$ consisting of all points $P$ lying in the first quadrant of the plane and satisfying $2 \leq d_1(P)+d_2(P) \leq 4$, is