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Question
Obtain the Cartesian equation for the locus of z = x + iy in the following cases:
|z – 4| = 16
Solution
Let z = x + iy
|x + iy – 4| – 16
|(x – 4) + iy| = 16
`sqrt((x - 4)^2 + y^2)` = 16
∴ Squaring on both sides
(x – 4)2 + y2 = 256
x2 – 8x + 16 + y2 – 256 = 0
x2 + y2 – 8x – 240 = 0
The locus of the point is a circle.
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