How do I find the equation of an ellipse?

Question

Given: the center of the ellipse is located at the origin and it passes through (1,3) and (2,2)

Answer 1

If you plot the 3 points you know, and then plot their opposites to form your ellipse, you can determine the major and minor vertices or your ellipse. Because your ellipse is taller than it is wide, the vertical is the major vertices. Then just fill in your data to the formula for that type of ellipse: x² / b² + y² / a² = 1 (a is the larger of the distance from the centerpoint to either the horizontal or vertical vertex, and b is the smaller). You can't really define a & b since they don't pass directly through a point, but you do know X and Y because you were given several points. Just plug those into the formula, and voila. Say you used (2,2). Your formula would become 4/b²+4/a²=1.

 

I hope that helps.

 

DISCLAIMER: I am not a math teacher, and would welcome clarification/correction from one.