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

$A$ variable line $\frac{x}{a}+\frac{y}{b}=1$ is such that $a+b=4$. The locus of the midpoint of the portion of the line intercepted between the axes is

$A$ straight line through the point of intersection of the lines $x+2y=4$ and $2x+y=4$ meets the coordinate axes at $A$ and $B$. The locus of the mid-point of $AB$ is

Through a given point $P(a, b)$,a straight line is drawn to meet the axes at $Q$ and $R$. If the parallelogram $OQSR$ is completed,then the equation of the locus of $S$ is (given $O$ is the origin):

$ABC$ is an isosceles triangle. If the coordinates of the base are $B(1, 3)$ and $C(-2, 7)$,the coordinates of vertex $A$ can be

If $A = (a, 0)$ and $B = (-a, 0)$,then the locus of a point $P = (x, y)$ such that $PA^2 - PB^2 = a^2$ is.