Let T₁ and T₂ be two distinct common tangents to the ellipse E:x²/6+y²/3=1 and the parabola P:y²=12x. Suppose that the tangent T₁ touches P and E at the points A₁ and A₂, respectively, and the tangent T₂ touches P and E at the points A₄ and A₃, respectively. Then which of the following statements is(are) true?