1. ## Ellipse Help

I am given 100 x-y (cartesian) coordinates for an ellipse. The ellipse slopes upward to the northeast and is centered off the origin at a given coordinate (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? Thanks.

2. Hello, sgorman!

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?
I can suggest an approach ... a rather long and tedious one.

The general quadratic function is: . $Ax^2 + Bxy + Cy^2 + Dx + Ey + F \;=\;0$

Use any six of the given points and set up a 6-by-6 system of equations.
. . Then solve for $A,B, C, D, E, F$

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.

3. Thank you for the response. Could you give me an example of how you would set up (and solve) each of the six equations using a hypothetical set of x-y coordinates? I don't mind the tedium -- I'm just not sure how this produces the answers I need.

4. I'm all set now -- thanks.