The equations of the perpendicular bisectors of the sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y+5=0$,respectively. If $A$ is $(1, -2)$,then the equation of the straight line $BC$ is

If the $y$-intercept of the perpendicular bisector of the line segment joining $P(1, 4)$ and $Q(k, 3)$ is $-4$,then a possible value of $k$ is

The foot of the perpendicular drawn from the origin to the line $3x + y = \lambda \, (\lambda \ne 0)$ is $P$. If the line meets the $x$-axis at $A$ and the $y$-axis at $B$,then the ratio $BP : PA$ is

The reflection of the point $(1, 1)$ along the line $y = -x$ is

Let $A \left(\frac{3}{\sqrt{a}}, \sqrt{a}\right)$ with $a > 0$ be a fixed point in the $xy$-plane. The image of $A$ in the $y$-axis is $B$,and the image of $B$ in the $x$-axis is $C$. If $D(3 \cos \theta, a \sin \theta)$ is a point in the fourth quadrant such that the maximum area of $\triangle ACD$ is $12$ square units,then $a$ is equal to:

The image of the point $(3,5)$ in the line $x-y+1=0$ lies on: