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Ellipse with semi-minor axis OB and foci S, S' where angle SBS' is a right angle: find the eccentricity

The same question, asked 2 times: 19 Apr 2025 S1, 13 May 2026 S1. Every wording below, oldest first.

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  1. Question 1

    19 Apr 2025 S1

    136
    An ellipse has OB as semi-minor axis, S and S′S^{'} are foci and angle SBS' is a right angle. Then the eccentricity of the ellipse is

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  2. Question 2

    13 May 2026 S1

    61
    In an ellipse with semi-minor axis OB, S and S' are its foci, a>ba > b and ∠SBS′\angle SBS' is a right angle, then the eccentricity of the ellipse is..

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