Question

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

Answer 1

Step 1:

Find the mid-point of the vertices

Let the coordinates of the mid-point = (x , y)

Vertices = ( -2, 0 ) and (2, 0)

`\begin{gathered} x\text{ = }\frac{-2\text{ + 2}}{2}\text{ = }(0)/(2)\text{ = 0} \\ y\text{ = }\frac{0\text{ + 0}}{2}\text{ = }(0)/(2)\text{ = 0} \end{gathered}`

Mid - point = ( 0, 0 ) = ( h, k)

Minor axis = 4

a = 2

b = 1

Final answer

`\begin{gathered} ((x-h)^2)/(b^2)\text{ + }((y-k)^2)/(a^2)\text{ = 1} \\ \end{gathered}`
`((x-0)^2)/(1^2)\text{ + }((y-0)^2)/(2^2)\text{ = 1}`
`(x^2)/(1)\text{ + }(y^2)/(4)\text{ = 1}`