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,

Let A(2, $$-$$3) and B($$-$$ 2, 1) be two angular points of $$\Delta$$ABC. If the centroid of the triangle moves on the line 2x + 3y = 1, then the locus of the angular point C is given by

The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = $$-$$ x to get the image point Q'. Then, the circumcentre of the $$\Delta$$PQQ' is

Let d₁ and d₂ be the lengths of the perpendiculars drawn from any point of the line $$7x - 9y + 10 = 0$$ upon the lines 3x + 4y = 5 and 12x + 5y = 7, respectively. Then,