The point Q is the image of the point P(1, 5) about the line y = x and R is the image of the point Q about the line y = $$-$$ X. The circumcentre of the $$\Delta$$PQR is

The angular points of a triangle are A($$-$$ 1, $$-$$ 7), B(5, 1) and C(1, 4). The equation of the bisector of the angle $$\angle $$ABC is

A line cuts the X-axis at A(5, 0) and the Y-axis at B(0, $$-$$3). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P and the Y-axis at Q. If AQ and BP meet at R, then the locus of R is

Transforming to parallel axes through a point (p, q), the equation $$2{x^2} + 3xy + 4{y^2} + x + 18y + 25 = 0$$ becomes $$2{x^2} + 3xy + 4{y^2} = 1$$. Then,