What geometric locus is described by |z - 3| = 2*|z + 3| in the complex plane?
Answer and explanation
Correct answer: C. A circle of Apollonius centered at (-5, 0) with radius 4
- Step 1: Let z = x + iy: (x - 3)^2 + y^2 = 4((x + 3)^2 + y^2). Step 2. Expand: x^2 - 6x + 9 + y^2 = 4(x^2 + 6x + 9 + y^2) => 3x^2 + 30x + 3y^2 + 27 = 0 => x^2 + 10x + y^2 + 9 = 0 => (x + 5)^2 + y^2 = 16. Answer: A circle of Apollonius centered at (-5, 0) with radius 4. Why not the others:* Ratio of distances to two fixed points equal to k != 1 is a Circle of Apollonius.
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