Finding the major and minor axises of an Ellipse knowing a certain point P and its eccentricity?

In a project I'm working on the user creates a circle and choose a point on that circle, P=(px,py). For the question's sake, let's assume 开发者_JAVA百科the center of the circle is at (0,0).

After the previous steps, the user can then change the eccentricity of the ellipse (as it was a circle it was actually an ellipse with e=0). While he changes the eccentricity, the ellipse should keep its center to (0,0), and the point P should stay on the ellipse's circumference.

Thanks! Aviad.

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If I made no mistake, the half axis of the ellipse are a = sqrt(x²+y²/(1-e²)) and b = a * sqrt(1-e²)

For the numeric eccentricity we have:

I) b = a * sqrt(1-e²)

and the equation for a point on the ellipse is:

II) x²/a² + y²/b² = 1

Substitue I) in II)

x²/a² + y²/(a² * (1-e²)) = 1

1/a² (x² + y²/(1-e²)) = 1

a² = (x² + y²/(1-e²))

a = sqrt(x² + y²/(1-e²))