If the common tangent to the parabolas,
y² = 4x and x² = 4y also touches the circle, x² + y² = c²,
then c is equal to :

Let the latus ractum of the parabola y² = 4x be the common chord to the circles C₁ and C₂ each of them having radius 2$$\sqrt 5 $$. Then, the distance between the centres of the circles C₁ and C₂ is :

Let P be a point on the parabola, y² = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is $${4 \over 3}$$, then :

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 :