The pair of lines represented by
$$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$ are perpendicular to each other for

The number of integer values of $$m$$, for which the $$x$$-coordinate of the point of intersection of the lines $$3x + 4y = 9$$ and $$y = mx + 1$$ is also an integer, is

Area of the parallelogram formed by the lines $$y = mx$$, $$y = mx + 1$$, $$y = nx$$ and $$y = nx + 1$$ equals

Let $$PS$$ be the median of the triangle with vertices $$P(2, 2),$$ $$Q(6, -1)$$ and $$R(7, 3).$$ The equation of the line passing through $$(1, -1)$$ and parallel to $$PS$$ is