If a point $P$ on the line $3x + 5y = 15$ is equidistant from the coordinate axes,then $P$ lies

Find the equation of a line passing through the point $(4, 3)$,which cuts a triangle of minimum area from the first quadrant.

The locus of a point $P(x, y)$ which moves in such a way that the segment $OP$,where $O$ is the origin $(0, 0)$,has a slope of $\sqrt{3}$ is:

$A$ straight line passing through a fixed point $(3, 5)$ intersects the coordinate axes at two points $A$ and $B$. If the locus of $C(x, y)$,which forms a rectangle with the points $A, O$ (origin),and $B$,is $ax + 2hxy + by = 0$,then $a + b + h =$

If the sum of the distances of a point $P(x, y)$ from two perpendicular lines in a plane is $1$,then the locus of $P$ is a

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: