How do you find the equation of an ellipse with major axis vertical and passes through points (0,4) and (2,0)?
This problem can only be done, if one assumes that two given points,
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 :
Equation  is the answer.
Here is a graph with the ellipse and the two points plotted: