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

$A$ point moves in the $x-y$ plane such that the sum of its distances from two mutually perpendicular lines is always equal to $3$. The area enclosed by the locus of the point is ............... $unit^{2}$.

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

If the vertices $P$ and $Q$ of a triangle $PQR$ are given by $(2, 5)$ and $(4, -11)$ respectively,and the point $R$ moves along the line $N: 9x + 7y + 4 = 0$,then the locus of the centroid of the triangle $PQR$ is a straight line parallel to

$A$ point $P$ on a line is at a distance of $4$ units from the origin $(0,0)$. If the line makes an angle of $60^{\circ}$ with the negative direction of the $X$-axis,then the coordinates of $P$ are

If the ends of the hypotenuse of a right-angled triangle are $(0, a)$ and $(a, 0)$,then the locus of the third vertex is: