Do I need foci to calculate an ellipse?I have been trying to find an answer, but where I look does not tell me why I need foci if I have all 4 vertices and the center. If I am just trying to create an ellipse with the 4 vertices and center, can I just plug the numbers into the equation of an ellipse without worrying about the foci? I am trying to understand how the foci come into play, as they don't appear in the actual equation of an ellipse. However, I want my ellipse to be correct. I am trying to take a circle, and scale the y axis only, elongating the circle to create the ellipse that still passes through the 4 points, 2 now scaled. It is a vertical ellipse.

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Do I need foci to calculate an ellipse?I have been trying to find an answer, but where I look does not tell me why I need foci if I have all 4 vertices and the center. If I am just trying to create an ellipse with the 4 vertices and center, can I just plug the numbers into the equation of an ellipse without worrying about the foci? I am trying to understand how the foci come into play, as they don&#039;t appear in the actual equation of an ellipse. However, I want my ellipse to be correct. I am trying to take a circle, and scale the y axis only, elongating the circle to create the ellipse that still passes through the 4 points, 2 now scaled. It is a vertical ellipse.

Kash Osborn · Accepted Answer

Step 1The general equation of an ellipse is a quadratic expression   a      x    2    +  2  b  x  y  +  c      y    2    +  d  x  +  e  y  +  f  =  0 where the foci do not appear explicitly.Step 2In the case of an axis-parallel ellipse, the cross term xy does not exist, and you can use the simplified form             (      x      −              x        c                    )        2                    a      2        +            (      y      −              y        c                    )        2                    b      2        =  1 where the center and axis lengths are explicit.

Wyatt Weeks · Accepted Answer

Explanation:You have 2a,2b from the given points. If you want to calculate an ellipse from relation             x      2              a      2        +            y      2              b      2        =  1 which has axes parallel to coordinate axes that is taken implied for your exercise, you can use   y  =  b      1    −          x      2              /              a      2       to find y for each x.(Foci location, latus rectum, eccentricity) are related parameters that is not required for above calculation).

If I am just trying to create an ellipse with the 4 vertices and center, can I just plug the numbers into the equation of an ellipse without worrying about the foci?

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