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

Answer:

The expression of the ellipse is: $\frac{x^2}{4} + y^2 = 1$

Step-by-step explanation:

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

$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$

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.

$2a = \sqrt{[2 - (-2)]^2}\\2a = \sqrt{(2 + 2)^2}\\2a = \sqrt{4^2}\\2a = 4\\a = 2$

Therefore the expression of the ellipse is:

$\frac{x^2}{2^2} + \frac{y^2}{1^2} = 1\\\\\frac{x^2}{4} + y^2 = 1$