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

Question

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, 2 , 3, 3 2 , 3 2, 4 2 , 2 2, 2 2 , 4 2

MARKS App · Accepted Answer

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

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