The locus of the point $P(x, y)$ such that the area of the $\triangle PAB$ is $7$,where $A(4, 5)$ and $B(-2, 3)$ are given points,is

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:

$A$ man standing on a railway platform noticed that a train took $21\,s$ to cross the platform (this means the time elapsed from the moment the engine enters the platform till the last compartment leaves the platform),which is $88\,m$ long,and that it took $9\,s$ to pass him. Assuming that the train was moving with uniform speed,what is the length of the train in meters?

$A$ straight line cuts off intercepts on the coordinate axes,the reciprocal of whose sum is $1/p$. Through which fixed point does this line always pass?

If the equation of the locus of a point equidistant from $(a_1, b_1)$ and $(a_2, b_2)$ is $(a_1 - a_2)x + (b_1 - b_2)y + c = 0$,find the value of $c$.

$A$ variable line through the point $P(-1, 2)$ cuts the coordinate axes at $A$ and $B$ respectively. If $Q$ is a point on $AB$ such that $PA, PQ, PB$ are in a harmonic progression,then the locus of $Q$ is