The equation of the straight line whose slope is $\frac{-2}{3}$ and which divides the line segment joining $(1,2),(-3,5)$ in the ratio $4: 3$ externally is

$7 x+y-24=0$ and $x+7 y-24=0$ represent the equal sides of an isosceles triangle. If the third side passes through $(-1,1)$ then, a possible equation for the third side is

The combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the point of intresection of the lines $x+2 y-3=0$ and $2 x-y-1=0$ is

If the line $2 x+b y+5=0$ forms an equilateral to triangle with $a x^{2}-96 b x y+k y^{2}=0$, then $a+3 k=$