- #1

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## Main Question or Discussion Point

Sketch the following region:

| z+i | + | z-1 | =2

I know that it is a ellipse, but i am trying to replace the z for x +iy.

I reached the following equation.

3x^2+3y^2 = 4x-4y+2xy

now how can a simplify it in order to have the ellipse equation: (x^2/a^2) + (y^2/b^2) = 1

| z+i | + | z-1 | =2

I know that it is a ellipse, but i am trying to replace the z for x +iy.

I reached the following equation.

3x^2+3y^2 = 4x-4y+2xy

now how can a simplify it in order to have the ellipse equation: (x^2/a^2) + (y^2/b^2) = 1