Suppose that the sides passing through the vertex $$(\alpha, \beta)$$ of a triangle are bisected at right angles by the lines $$y^2-8 x y-9 x^2=0$$. Then, the centroid of the triangle is

Suppose $$P$$ and $$Q$$ are the mid-points of the sides $$A B$$ and $$B C$$ of a triangle where $$A(1,3), B(3,7)$$ and $$C(7,15)$$ are vertices. Then, the locus of $$R$$ satisfying $$A C^2+Q R^2=P R^2$$ is

If the points of intersection of the coordinate axes and $$|x+y|=2$$ form a rhombus, then its area is

Suppose, in $$\triangle A B C, x-y+5=0, x+2 y=0$$ are respectively the equations of the perpendicular bisectors of the sides $$A B$$ and $$A C$$. If $$A$$ is $$(1,-2)$$, the equation of the line joining $$B$$ and $$C$$ is