The set of all points that forms a triangle of area $15$ sq units with the points $(1, -2)$ and $(-5, 3)$ lies on

$A$ 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?

If the equation to the locus of points equidistant from the points $(-2, 3)$ and $(6, -5)$ is $a x + b y + c = 0$,where $a > 0$,then the ascending order of $a, b, c$ is

The locus of a point which moves so that it is always equidistant from the points $A(a, 0)$ and $B(-a, 0)$ is

The locus of the orthocentre of the triangle formed by the lines $(1+p) x-p y+p(1+p)=0$,$(1+q) x-q y+q(1+q)=0$,and $y=0$,where $p \neq q$,is

If for a variable line $\frac{x}{a} + \frac{y}{b} = 1$,the condition $\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2}$ ($c$ is a constant) is satisfied,then the locus of the foot of the perpendicular drawn from the origin to the line is: