The area (in sq. units) of an equilateral triangle inscribed in the parabola y² = 8x, with one of its vertices on the vertex of this parabola, is :

If one end of a focal chord AB of the parabola y² = 8x is at $$A\left( {{1 \over 2}, - 2} \right)$$, then the equation of the tangent to it at B is :

The locus of a point which divides the line segment joining the point (0, –1) and a point on the parabola, x² = 4y, internally in the ratio 1 : 2, is :

If y = mx + 4 is a tangent to both the parabolas, y² = 4x and x² = 2by, then b is equal to :