Try dragging the points on the right to change the foci of the ellipse:

f=1+1*i

g=-1-(1*i)

The distance between two points is given by

function('Distance',a,b)=abs(a-b)

The ellipse is constructed as the locus of all points p whose distance to f and g sum to n.

p=x+i*y

function('Distance',p,f)+function('Distance',p,g)=n

abs(g-f)

When f = g, we get a circle as a special case of the ellipse.

Note that when n is less than the distance between the foci, no points can satisfy the equation so there is no ellipse.

Graph of the formula

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