If the equation of the median through vertex $A(3, k)$ of $\triangle ABC$ with vertices $B(2, 1)$ and $C(-4, 5)$ is $x + 4y = p$,then $k = ?$ where $p$ and $k$ are constants.

What is the circumcenter of the triangle with vertices $(0, 0)$,$(3, 0)$,and $(0, 4)$?

The vertices of a triangle are $(6,0), (0,6)$ and $(6,6)$. The distance between its circumcentre and centroid is

In a triangle $PQR$,the coordinates of the points $P$ and $Q$ are $(-2, 4)$ and $(4, -2)$ respectively. If the equation of the perpendicular bisector of $PR$ is $2x - y + 2 = 0$,then the centre of the circumcircle of the $\Delta PQR$ is

If the orthocentre of the triangle,whose vertices are $(1,2), (2,3)$ and $(3,1)$ is $(\alpha, \beta)$,then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$ is:

The orthocentre of the triangle with vertices $(0, 0)$,$(3, 4)$,and $(4, 0)$ is