Equation of Ellipse in Complex Plane/Examples/Foci at -3, 3, Major Axis 10

Example of Equation of Ellipse in Complex Plane
The ellipse in the complex plane whose major axis is of length $10$ and whose foci are at the points corresponding to $-3$ and $3$ is given by the equation:
 * $\cmod {z + 3} + \cmod {z - 3} = 10$

and also as:


 * $\dfrac {x^2} {25} + \dfrac {y^2} {16} = 1$

Proof
From Equation of Ellipse in Complex Plane, the ellipse whose major axis is $d$ and whose foci are at the points corresponding to $\alpha$ and $\beta$ is given by:
 * $\cmod {z - \alpha} + \cmod {z - \beta} = d$


 * Equation of Ellipse in Complex Plane-Examples-Foci at -3, 3, Major Axis 10.png

The rest of the result follows from Equation of Ellipse in Reduced Form: Cartesian Frame.