Answer:
![\frac{x^2}{4} +\frac{y^2}{25} =1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B4%7D%20%2B%5Cfrac%7By%5E2%7D%7B25%7D%20%3D1)
Step-by-step explanation:
From a sketch of the given coordinates, you notice that the ellipse has its center at (0,0) i.e origin
It is a vertical ellipse centered at (0,0),
The major axis has its coordinates at (0,a) = (0,5) and (0,-a) =(0,-5)
The minor axis has it coordinates at (0,b)=(0,-2) and (0,2)
Here a>b
The length of major axis is 2a = 2*5= 10
The length of minor axis is 2b= 2*2=4
Equation is given by
![\frac{x^2}{b^2} +\frac{y^2}{a^2} =1\\\\\\\frac{x^2}{2^2} +\frac{y^2}{5^2} =1\\](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Bb%5E2%7D%20%2B%5Cfrac%7By%5E2%7D%7Ba%5E2%7D%20%3D1%5C%5C%5C%5C%5C%5C%5Cfrac%7Bx%5E2%7D%7B2%5E2%7D%20%2B%5Cfrac%7By%5E2%7D%7B5%5E2%7D%20%3D1%5C%5C)