The length of the chord of the parabola x² $$=$$ 4y having equation x – $$\sqrt 2 y + 4\sqrt 2 = 0$$  is -

If the parabolas y² = 4b(x – c) and y² = 8ax have a common normal, then which on of the following is a valid choice for the ordered triad (a, b, c)?

Let A(4, $$-$$ 4) and B(9, 6) be points on the parabola, y² = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of $$\Delta $$ACB is maximum. Then, the area (in sq. units) of $$\Delta $$ACB, is :

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?