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
