Given an elliptic curve in generalised Weierstrass form
y^2 + a1*xy + a3*y = x^3 + a2*x^2 + a4*x + a6
and a point P=(x,y) which is not the point at infinity.
How exactly do I show that -P is (x, -a1x - a3 - y)?
**Hint: This involves solving a quadratic in y, also the sum of the roots of a monic quadratic polynomial equals the negative of the coefficient of the linear term.
Any help at all would be greatly appreciated.