Major and Minor Axis of Ellipse – Length and Formula

Here you will learn formula to find the length of major axis of ellipse and minor axis of ellipse with examples.

Let’s begin –

Major and Minor Axis of Ellipse

(i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b

Length of the major axis = 2a

Length of the minor axis = 2b

Equation of major axis is y = 0

Equation of minor axis is x = 0

(ii) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a < b

Length of the major axis = 2b

Length of the minor axis = 2a

Equation of major axis is x = 0

Equation of minor axis is y = 0

Also Read : Different Types of Ellipse Equations and Graph

Example : For the given ellipses, find the length of major and minor axes.

(i)  \(16x^2 + 25y^2\) = 400

(ii)  \(x^2 + 4y^2 – 2x\) = 0

Solution :

(i)  We have,

\(16x^2 + 25y^2\) = 400 \(\implies\) \(x^2\over 25\) + \(y^2\over 16\),

where \(a^2\) = 25 and \(b^2\) = 16 i.e. a = 5 and b = 4

Clearly a > b,

Therefore, Length of the Major Axis = 2a = 10

And Length of Minor Axis = 2b = 8

(ii) We have,

\(x^2 + 4y^2 – 2x\) = 0

\(\implies\) \((x – 1)^2\) + 4\((y – 0)^2\) = 1

\(\implies\)  \((x – 1)^2\over 1^2\) + \((y – 0)^2\over (1/2)^2\) = 1

Here, a = 1 and b = 1/2

Clearly a > b,

Therefore, Length of the Major Axis = 2a = 2

And Length of Minor Axis = 2b = 1

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