Ellipse

Easymathematics

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

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x²/a² + y²/b² = 1 (a > b)

x²/b² + y²/a² = 1 (a > b)

x² + y² = a²

x²/a² - y²/b² = 1

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Subject: mathematics
Chapter: coordinate geometry
Topic: ellipse
Difficulty: Easy
Year: 2025

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x²/a² + y²/b² = 1 (a > b)

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

This easy difficulty mathematics question is from the chapter coordinate geometry, covering the topic of ellipse. It appeared in the 2025 exam.

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