Finding the foci of an ellipse

Question

Let's say we have the following figure

where $ζ$ is the major axis, $Ε$ is one foci, $ε$ is a tangent and $Μ$ a point of the plane. Also, I don't know how to call $κ$ in English, but it's the circle with center Ε..

Can someone tell me how I can find where $E'$, the second foci, is on the axis $ζ$?

Thank you in advance.

Answer 1

HINT

J = center of ellipse

Radius of circle = a

E1 '= second focus