If $2a + b + 3c = 0$,then the line $ax + by + c = 0$ passes through the fixed point that is

Two points $A(-a, 0)$ and $B(a, 0)$ are given. If $C$ is a variable point lying on one side of the line $AB$ such that $\angle CAB - \angle CBA = \alpha$,where $\alpha$ is a positive constant,then the locus of the point $C$ is

$A(1, 0)$,$B(0, 2)$,and $C(1, 2)$ are three points on the $XY$-plane. If a point $P(x, y)$ moves such that the area of $\triangle PAB$ is twice the area of $\triangle ABC$,then the locus of the point $P$ is:

If the sum of the distances of a point from two perpendicular lines in a plane is $1$,find its locus.

The point $P$ is equidistant from $A(1, 3)$,$B(-3, 5)$,and $C(5, -1)$. Then $PA$ is equal to:

$A$ point on the straight line $3x + 5y = 15$ which is equidistant from the coordinate axes will lie in