For the ellipse x² + 4y² = 4, the tangent and normal at a point P(theta) meet the major axis at Q and R respectively. Given QR = 2 and the eccentric angle theta satisfies cos theta = +/-(a/b) with a, b coprime positive integers, find 2b/a.

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Accepted Answer

3. Setting the separation of the major-axis intercepts equal to 2 gives cos theta = 2/3, so a = 2, b = 3 and 2b/a = 3.

For the ellipse x² + 4y² = 4, the tangent and normal at a point P(theta) meet the major axis at Q and R respectively. Given QR = 2 and the eccentric angle theta satisfies cos theta = +/-(a/b) with a, b coprime positive integers, find 2b/a.

Solution

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