The coordinates of a point $P$ on the line $2x - y + 5 = 0$ such that $|PA - PB|$ is maximum,where $A$ is $(4, -2)$ and $B$ is $(2, -4)$,are:

Let $A(-1,1)$ and $B(2,3)$ be two points and $P(x,y)$ be a variable point above the line $AB$ such that the area of $\triangle PAB$ is $10$. If the locus of $P$ is $ax+by=15$,then $5a+2b$ is:

If a straight line drawn through the point of intersection of the lines $4x + 3y - 1 = 0$ and $3x + 4y - 1 = 0$ meets the coordinate axes at the points $P$ and $Q$,then the locus of the midpoint of $PQ$ is:

$A$ point $P$ moves on the line $2x - 3y + 4 = 0$. If $Q(1, 4)$ and $R(3, -2)$ are fixed points,then the locus of the centroid of $\Delta PQR$ is a line

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

$A$ straight line through the point $(1, 1)$ meets the $x$-axis at $A$ and the $y$-axis at $B$. The locus of the mid-point of $AB$ is