# Ellipse: Minor Axis

How to find the minor axis of an ellipse: formulas, examples, and their solutions.

## Formula: If *a* > *b*

For the ellipse *x*^{2}/*a*^{2} + *y*^{2}/*b*^{2} = 1,

if *a* > *b*,

then the minor axis (= shortest diamter)

is the vertical diameter.

So the minor axis is 2*b*.

Major axis - Formula (*a* > *b*)

## Example 1: Minor Axis of *x*^{2}/25 + *y*^{2}/16 = 1

Change the equation in standard form.

25 = 5^{2}

16 = 4^{2}

So *x*^{2}/5^{2} + *y*^{2}/4^{2} = 1.

*a* > *b* (5 > 4)

So the minor axis is 2⋅4.

2⋅4 = 8

So (minor axis) = 8.

This is the graph of *x*^{2}/5^{2} + *y*^{2}/4^{2} = 1.*a* > *b*

So the minor axis, 8,

is the vertical diameter.

## Formula: If *a* < *b*

For the ellipse *x*^{2}/*a*^{2} + *y*^{2}/*b*^{2} = 1,

if *a* < *b*,

then the minor axis (= shortest diamter)

is the horizontal diameter.

So the minor axis is 2*a*.

Major axis - Formula (*a* < *b*)

## Example 2: Minor Axis of 9*x*^{2} + 4*y*^{2} = 36

Change the equation in standard form.

Divide both sides by 36.

9/36 = 1/4

4/36 = 1/9

4 = 2^{2}

9 = 3^{2}

So *x*^{2}/2^{2} + *y*^{2}/3^{2} = 1.

*a* < *b* (2 < 3)

So the minor axis is 2⋅2.

2⋅2 = 4

So (minor axis) = 4.

This is the graph of *x*^{2}/2^{2} + *y*^{2}/3^{2} = 1.*a* < *b*

So the minor axis, 4,

is the horizontal diameter.