$A$ straight line moves such that the sum of the reciprocals of its intercepts on two perpendicular lines is constant. Then the line always passes through:

$A$ point moves in the $XY$-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 that point is (in sq. units)

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

$A$ line moves such that the portion of it intercepted between the coordinate axes is of constant length $a$. Then,the locus of the midpoint of that line segment is

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:

$A$ rod of length $8$ units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$ and $y+2=0$,respectively. If the locus of the point $P$,that divides the rod $AB$ internally in the ratio $2:1$ is $9(x^2+\alpha y^2+\beta xy+\gamma x+28y)-76=0$,then $\alpha-\beta-\gamma$ is equal to :