The locus of the mid-point of the line segment joining the focus of the parabola y² = 4ax to a moving point of the parabola, is another parabola whose directrix is :

The centre of the circle passing through the point (0, 1) and touching the parabola
y = x² at the point (2, 4) is :

Let L₁ be a tangent to the parabola y² = 4(x + 1)
and L₂ be a tangent to the parabola y² = 8(x + 2)
such that L₁ and L₂ intersect at right angles. Then L₁ and L₂ meet on the straight line :

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