complex variables : Triangle inequality

[Benzoate]

1. The problem statement, all variables and given/known data

Using the fact that |z(1)-z(2)| is the distance between two points z(1) and z(2) , give a geometric argument that

a)|a-4*i| + |z+4*i| =10 represents an ellipse whose foci are (0,4) and(0,-4).

2. Relevant equations

Triangle inequality equation; distance formula


3. The attempt at a solution

|z(1)-z(2)|=sqrt((0-0)^2 + (4-(-4))^2)= 8 . How is the Radius =10 of the equation related to the distance between z(1) and z(2) which I calculated to be 8. If there is a relationship between the distance formula and the radius, how will the relationship between the radius and the distance between the two points help me determined if|z-4i| + |z+4i|=10 represents an ellipse with foci (0,4) and (0,-4).

[NoMoreExams]

You calculated the distance between the foci didn't you? The foci don't lie on the contour of the ellipse. Besides how are you defining radius for an ellipse?

[Benzoate]

You calculated the distance between the foci didn't you? The foci don't lie on the contour of the ellipse. Besides how are you defining radius for an ellipse?

I don't think there is a radius for an ellispse. But what variable of the ellipse is 10 supposed to represent? distance between the foci is 8.