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How do I calculate the length of the major axis of an ellipse? I have the eccentricity and the length of the semi-major axis.

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3 Answers

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Multiply the semi-major axis by 2, and that's the major axis.

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As wikipedia points out, the eccentricity $\epsilon$ of an ellipse obeys the equation $$\epsilon=\sqrt{1-\left(\frac{b}{a}\right)^2}$$ where $a$ and $b$ are respectively the semi-major and semi-minor axes of the ellipse.

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The semi-minor axis $b$ of an ellipse can be found by the equation$${b}=\sqrt{{a}^2(1-\epsilon^2)}$$

where $a$ and $\epsilon$ are respectively the semi-major axis and eccentricity of the ellipse.

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