The orthocentre of the triangle formed by the lines $$xy=0$$ and $$x+y=1$$ is

The equations to a pair of opposites sides of parallelogram are $${x^2} - 5x + 6 = 0$$ and $${y^2} - 6y + 5 = 0,$$ the equations to its diagonals are

The locus of a variable point whose distance from $$\left( { - 2,\,0} \right)$$ is $$2/3$$ times its distance from the line $$x = - {9 \over 2}$$ is

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is