Major Axis of an Ellipse

High School

Definition

The principle axis of symmetry in an ellipse. It is a line that passes through the vertices, center, and the foci of an ellipse. It can also be considered the longest diameter that can be measured in an ellipse. One half of a major axis is called a the semi-major axis.

Worked examples

\(\frac{x^2}{25} + \frac{y^2}{9} = 1\)

The major axis is horizontal with length \(2a = 10\) because \(a^2 = 25 > b^2 = 9\).

\(\frac{x^2}{16} + \frac{y^2}{36} = 1\)

The major axis is vertical with length \(2a = 12\) because \(a^2 = 36 > b^2 = 16\).

Common mistakes

\(\frac{x^2}{9} + \frac{y^2}{25} = 1\) has horizontal major axis → The major axis is vertical because \(25 > 9\) The major axis runs along the direction of the larger denominator, not just the x-term.
Semi-major axis \(a = 25\) from \(\frac{x^2}{25} + \frac{y^2}{9} = 1\) → Semi-major axis \(a = 5\) because \(a = \sqrt{25}\) The denominator is a², not a itself.
Major axis length equals \(a\) → Major axis length equals \(2a\) The major axis spans from vertex to vertex through the center, so it is twice the semi-major axis.

Where you'll use it next

You'll use the major axis when graphing ellipses, finding foci with \(c^2 = a^2 - b^2\), and solving conic section problems in precalculus and calculus, as well as in physics applications like planetary orbits.

Found in 1 StudyPug lesson

Conics - Ellipse

Grade 12 Math

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