# How do you write an equation of a ellipse with vertices (0,2), (4,2), and endpoints of the minor axis (2,3), (2,1)?

##### 1 Answer

#### Answer:

#### Explanation:

Here we have an ellipse with vertices at

The equation of an ellipse centred at the origin with major axis length

Here we have an ellipse with major axis on

(Since the vertices are both on

And minor axis on

(Since the endpoints of the minor axis are both on

Hence, the centre of the ellipse is at

From the above we can calculate the length of the major axis to be:

and the length of the minor axis to be:

Applying the shifts of the centre from

Substituting for

Hence, the equation of our ellipse is:

We can see this ellipse in the graphic below that satisfies the given conditions.

graph{(x-2)^2/4+(y-2)^2/1=1 [-3.26, 7.84, -0.51, 5.04]}