The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x² such that the rectangle lies inside the parabola, is :

If the area of the triangle whose one vertex is at the vertex of the parabola, y² + 4(x – a²) = 0 and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :

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)?