The vertices of $\Delta PQR$ are $P (2,1), Q (-2,3)$ and $R (4,5) .$ Find equation of the median through the vertex $R$.

Two mutually perpendicular straight lines through the origin from an isosceles triangle with the line $2x + y = 5$ . Then the area of the triangle is :

The co-ordinates of the vertices $A$ and $B$ of an isosceles triangle $ABC (AC = BC)$ are $(-2,3)$ and $(2,0)$ respectively. $A$ line parallel to $AB$ and having a $y$ -intercept equal  to $\frac{43}{12}$ passes through $C$, then the co-ordinates of $C$ are :-

A point moves so that square of its distance from the point $(3, -2)$ is numerically equal to its distance from the line $5x – 12y = 13$. The equation of the locus of the point is

The triangle $PQR$ is inscribed in the circle ${x^2} + {y^2} = 25$. If $Q$ and $R$ have co-ordinates $(3,4)$ and $(-4, 3)$ respectively, then $\angle QPR$ is equal to