A straight the through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q.$ If $O$ is the origin and the rectangle $OPRQ$ is completed, then the locus of $R$ is:

Area of the rhombus bounded by the four lines, $ax \pm by \pm c = 0$ is :

The area of triangle formed by the lines $x + y - 3 = 0 , x - 3y + 9 = 0$ and $3x - 2y + 1= 0$

One side of a rectangle lies along the line $4x + 7y + 5 = 0.$ Two of its vertices are $(-3, 1)$ and $(1, 1)$. Then the equations of other three sides are

The triangle $PQR$ is inscribed in the circle ${x^2} + {y^2} = 25$. If $Q$ and $R$ have co-ordinates $(3,4)$ and $(-4, 3)$ respectively, then $\angle QPR$ is equal to

In a triangle $ABC$, coordianates of $A$ are $(1, 2)$ and the equations of the medians through $B$ and $C$ are $x + y = 5$ and $x = 4$ respectively. Then area of $\Delta ABC$ (in sq. units) is