The focal chord of the parabola y 2 = 32 x touches the ellipse x 2 4 2 + y 2 2 2 = 1 in the first quadrant at the point

Step-by-step solution

Let the tangent to the ellipse at 4 cos ⁡ θ , 2 sin ⁡ θ be x cos ⁡ θ 4 + y sin ⁡ θ 2 = 1 ∵ it passes through the focus 8,0 ⇒ cos ⁡ θ = 1 2 ⇒ θ = π 3 ⇒ point is 4 2 , 2 3 2 ≡ 2 , 3