Question

the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?​

Answer 1

The equation for this ellipse is
`(x^(2))/(64) + (y^(2))/(16) = 1`.

Explanation:

The standard equation of the ellipse is described by the following expression:

`(x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1`

Where
`a` and
`b` are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal,
`a > b`. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)

`(x^(2))/(64) + (y^(2))/(16) = 1`

The equation for this ellipse is
`(x^(2))/(64) + (y^(2))/(16) = 1`.