Hello, sgorman!

I can suggest an approach ... a rather long and tedious one.I am given 100 x-y (cartesian) coordinates for an ellipse.

The ellipse slopes upward to the northeast and is centered at (h, k).

I need to find the two vertices (x-y coordinates) of the major axis.

Can you tell me how to do this using only the information supplied?

The general quadratic function is: .

Use anysixof the given points and set up a 6-by-6 system of equations.

. . Then solve for

Once we have the equation of the ellipse, we can determine the angle

. . through which it is rotated and then the endpoints of its major axis.