The equation of a curve is \(3x^2 + 4xy + 3y^2 = 5\).

(a) Show that \(\frac{dy}{dx} = -\frac{3x + 2y}{2x + 3y}\).

(b) Hence find the exact coordinates of the two points on the curve at which the tangent is parallel to \(y + 2x = 0\).