Question

Find the equation of the following ellipse based on the following information: Vertices: (-2,0), (2,0) minor axis of length 2​

Answer 1

The expression of the ellipse is:
`(x^2)/(4) + y^2 = 1`

Explanation:

The equation of a ellipse can be written by the following expression:

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

Where 2a is the length of the major axis and 2b is the length of the minor axi. Since we were given the length of the minor vertex, then:

`2b = 2\\b = 1`

The length of the major axis is the distance between the two vertices.

`2a = √([2 - (-2)]^2)\\2a = √((2 + 2)^2)\\2a = √(4^2)\\2a = 4\\a = 2`

Therefore the expression of the ellipse is:

`(x^2)/(2^2) + (y^2)/(1^2) = 1\\\\(x^2)/(4) + y^2 = 1`