The equation |z - 5i| / |z + 5i| = 12, where | vedclass

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(A) Given the equation: $\frac{|z - 5i|}{|z + 5i|} = 12$ Squaring both sides: $\frac{|z - 5i|^2}{|z + 5i|^2} = 144$ Substituting $z = x + iy$: $\frac{

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Circle

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(A) Given the equation: $\frac{|z - 5i|}{|z + 5i|} = 12$ Squaring both sides: $\frac{|z - 5i|^2}{|z + 5i|^2} = 144$ Substituting $z = x + iy$: $\frac{x^2 + (y - 5)^2}{x^2 + (y + 5)^2} = 144$ $x^2 + y^2 - 10y + 25 = 144(x^2 + y^2 + 10y + 25)$ $x^2 + y^2 - 10y + 25 = 144x^2 + 144y^2 + 1440y + 3600$ $143x^2 + 143y^2 + 1450y + 3575 = 0$ This is an equation of the form $x^2 + y^2 + 2gx + 2fy + c = 0,$ which represents a circle.

The equation $|z - 5i| / |z + 5i| = 12,$ where $z = x + iy,$ represents a/an

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