Ellipse: Minor Axis

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 diameter) is 2b.

For the ellipse x2/a2 + y2/b2 = 1,

if a > b,
then the minor axis (= shortest diamter)
is the vertical diameter.

So the minor axis is 2b.

Major axis - Formula (a > b)

Example 1: Minor Axis of x2/25 + y2/16 = 1

Find the minor axis of the given ellipse. x^2/25 + y^2/16 = 1

Change the equation in standard form.

25 = 52
16 = 42

So x2/52 + y2/42 = 1.

a > b (5 > 4)

So the minor axis is 2⋅4.

2⋅4 = 8

So (minor axis) = 8.

This is the graph of x2/52 + y2/42 = 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 diameter) is 2a.

For the ellipse x2/a2 + y2/b2 = 1,

if a < b,
then the minor axis (= shortest diamter)
is the horizontal diameter.

So the minor axis is 2a.

Major axis - Formula (a < b)

Example 2: Minor Axis of 9x2 + 4y2 = 36

Find the minor axis of the given ellipse. 9x^2 + 4y^2 = 36

Change the equation in standard form.

Divide both sides by 36.

9/36 = 1/4

4/36 = 1/9

4 = 22
9 = 32

So x2/22 + y2/32 = 1.

a < b (2 < 3)

So the minor axis is 2⋅2.

2⋅2 = 4

So (minor axis) = 4.

This is the graph of x2/22 + y2/32 = 1.

a < b

So the minor axis, 4,
is the horizontal diameter.