Let L be a tangent line to the parabola y² = 4x $$-$$ 20 at (6, 2). If L is also a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$$, then the value of b is equal to :

Let C be the locus of the mirror image of a point on the parabola y² = 4x with respect to the line y = x. Then the equation of tangent to C at P(2, 1) is :

If the three normals drawn to the parabola, y² = 2x pass through the point (a, 0) a $$\ne$$ 0, then 'a' must be greater than :

The shortest distance between the line x $$-$$ y = 1 and the curve x² = 2y is :