Calculating major axis of an ellipse

Question

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.

Answer 1

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.

Answer 2

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

Answer 3

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.