# 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

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