Question

Major and minor axis of the ellipse

Answer 1

Length of Major Axis: 6√2

Length of Minor Axis: 4√2

Explanation:

The general equation of the ellipse is:
`$ (x^2)/(a^2) + (y^2)/(b^2) = 1 $` where
`$ a > b $`.

Then the major axis is along
`$ x - axis $`.

If the equation of the ellipse of of the form
`$ (x^2)/(b^2) + (y^2)/(a^2) = 1 $` where
`$ a > b $`.

In this case, the equation of the major axis is along the
`$ y - axis $`.

Here, the given equation of the second form.

The length of the major axis = 2a

The length of the minor axis = 2b

The given equation of the ellipse is:

`$ ((x - 3)^2)/(18) + ((y + 4)^2)/(32) = 1 $`

Therefore,
`$ a^2 = 32 $` and
`$ b^2 = 18 $`.

The length of the major axis = 2(√32) = 6√2

The length of the minor axis = 2(√18) = 4√2