Let P(at², 2at), Q, R(ar², 2ar) be three points on a parabola y² = 4ax. If PQ is the focal chord and PK, QR are parallel where the co-ordinates of K is (2a, 0), then the value of r is

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