If the angle between the pair of lines given by the equation $a x^{2}+4 x y+2 y^{2}=0$ is $45^{\circ}$, then the possible values of $a$

By shifting the origin to the point $(h, 5)$ by the translation of coordinate axes, if the equation $y=x^{3}-9 x^{2}+c x-d$ transforms to $Y=X^{3}$, then $\left(d-\frac{c}{h}\right)=$

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