The perpendicular distance of the $Y$-axis from the point $(-2, 5)$ is.......

If the vertices of $\Delta ABC$ are $A(0, 0)$,$B(4, 0)$ and $C(0, 6)$,then the coordinates of the point $P$ which is equidistant from $A, B$ and $C$ and in the plane of $\Delta ABC$ is $\ldots \ldots \ldots$

If the vertices of $\Delta ABC$ are $A(1, 4)$,$B(-3, 2)$,and $C(5, 0)$,then the length of the median $\overline{AD}$ is.........

Find the circumcentre of the triangle with vertices $(4,6), (5,1),$ and $(4,0)$.

The points $A(2, 9)$,$B(a, 5)$,and $C(5, 5)$ are the vertices of a triangle $ABC$ right-angled at $B$. Find the value of $a$ and the area of $\triangle ABC$.

The perpendicular bisector of the line segment joining the points $A(1, 5)$ and $B(4, 6)$ cuts the $y$-axis at