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

For the variable $t$, the locus of the point of intersection of the lines $3tx - 2y + 6t = 0$ and $3x + 2ty - 6 = 0$ is

$A$ line cuts the $x$-axis at $A(7, 0)$ and the $y$-axis at $B(0, -5)$. $A$ variable line $PQ$ is drawn perpendicular to $AB$ cutting the $x$-axis at $P(a, 0)$ and the $y$-axis at $Q(0, b)$. If $AQ$ and $BP$ intersect at $R(h, k)$, the locus of $R$ is

$A$ variable line passes through a fixed point $(a, b)$ and meets the coordinate axes at $A$ and $B$. The locus of the point of intersection of lines drawn through $A$ and $B$ parallel to the coordinate axes is:

The locus of the centroid of a triangle whose vertices are $(1, 0)$,$(a \cos t, a \sin t)$,and $(b \sin t, -b \cos t)$ is $9x^2 + 9y^2 - 6x = k$. Then,the value of $k$ is equal to

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