ellipse

Question

The standard equation of an ellipse with major axis along x-axis is

RankGuru · Accepted Answer

1. **Definition**: An ellipse is the locus where the sum of distances from two foci is constant.
2. **Axis Geometry**: If the semi-major axis is $a$ (along x) and the semi-minor axis is $b$ (along y), the equation is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.
3. **Constraint**: For the major axis to be along the x-axis, the denominator of $x^2$ must be larger, hence **$a > b$**.
4. **Properties**: Foci are at $(\pm ae, 0)$, where $e = \sqrt{1 - b^2/a^2}$.

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