Consider the parabola y² = 4x. Let P and Q be points on the parabola where P(4, $$-$$ 4) and Q(9, 6). Let R be a point on the arc of the parabola between P and Q. Then, the area of $$\Delta$$PQR is largest when

The axis of the parabola $${x^2} + 2xy + {y^2} - 5x + 5y - 5 = 0$$ is

A line passing through the point of intersection of x + y = 4 and x $$-$$ y = 2 makes an angle $${\tan ^{ - 1}}\left( {{3 \over 4}} \right)$$ with the X-axis. It intersects the parabola $${y^2} = 4(x - 3)$$ at points $$({x_1},{y_1})$$ and $$({x_2},{y_2})$$, respectively. Then, $$|{x_1},{y_2}|$$ is equal to

If the vertex of the conic $${y^2} - 4y = 4x - 4a$$ always lies between the straight lines $$x + y = 3$$ and $$2x + 2y - 1 = 0$$, then