The shortest distance between the line y = x and the curve y² = x – 2 is :

The equation of a tangent to the parabola, x² = 8y, which makes an angle $$\theta $$ with the positive directions of x-axis, is :

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 :

Let P(4, –4) and Q(9, 6) be two points on the parabola, y² = 4x and let x be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of $$\Delta $$PXQ is maximum. Then this maximum area (in sq. units) is :