If the points $A(3, 4)$,$B(7, 7)$,and $C(a, b)$ are collinear and $AC = 10$,then $(a, b) =$

$A$ straight line meets the $X$ and $Y$ axes at the points $A$ and $B$ respectively. If $AB = 6$ units,then the locus of the point $P$ which divides the line segment $AB$ such that $AP : PB = 2 : 1$ is

$A$ variable line passes through a fixed point $(x_{1}, y_{1})$ and meets the axes at $A$ and $B$. If the rectangle $OAPB$ is completed, the locus of $P$ is, ($O$ being the origin of the system of axes).

If $A=(5,3)$,$B=(3,-2)$ and a point $P$ is such that the area of the triangle $PAB$ is $9$,then the locus of $P$ represents

The line $AB$ cuts off equal intercepts $2a$ from the axes. From any point $P$ on the line $AB$, perpendiculars $PR$ and $PS$ are drawn to the axes. The locus of the mid-point of $RS$ is

$A$ line is drawn through the point $(1, 2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a $\triangle OPQ$,where $O$ is the origin. If the area of $\triangle OPQ$ is least,then the slope of the line $PQ$ is