how to identify parabola, ellipse , circle etc, when a complex number equation is given ??

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how to identify parabola, ellipse , circle etc, when a complex number equation is given ??

Mathematics
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circle: \[x^2 + y^2 = Z\] Ellipse: when a and b vary\[ax^2 + by^2 = Z\]
where Z is a number
question: the set of point Z is satisfying | Z + 4| + |Z - 4| = 0, now how to identify that this is ellipse ???

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Other answers:

i know answer that it is an ellispe with e = 3/4 but dont know how to solve it

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