AL Co-geometry

1. It is given that a line y = mx + c touches the ellipse (E) : x^2/a^2 + y^2/b^2 = 1 if and only if c^2 = a^2m^2 + b^2.

Show that if (p,q) is a point such that p^2 =/= q^2 and b^2p^2 + a^2q^2 > a^2b^2, then the equation of the pair of tangents from (p,q) to (E) is (qx-py)^2 = a^2(y-q)^2 + b^2(x-p)^2

2. Prove that the equation √x + √y = √a, where a is a positive constant, represents a parabola.