# How do you find the equation of an ellipse with major axis vertical and passes through points (0,4) and (2,0)?

##### 1 Answer

This problem can only be done, if one assumes that two given points,

#### Explanation:

The general Cartesian equation for an ellipse with a vertical major axis is:

Where x and y correspond any point,

Using the previously stated assumption.

The upper vertex on the major axis will have the coordinates:

The right vertex on the minor axis will have the coordinates:

Matching these two point to the given points:

This allows us to write the following equations:

Substituting 0 for h and k:

Substitute these 4 values into equation [1]:

Equation [2] is the answer.

Here is a graph with the ellipse and the two points plotted: