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प्रश्न
Obtain the Cartesian equation for the locus of z = x + iy in the following cases:
|z – 4|2 – |z – 1|2 = 16
उत्तर
|x + iy – 4|2 – |x + iy – 1|2 = 16
⇒ |(x – 4) + iy|2 – |(x – 1) + iy|2 = 16
⇒ [(x – 4)2 + y2] – [(x – 1)2 + y2] = 16
⇒ (x2 – 8x + 16 + y2) – (x2 – 2x + 1 + y2) = 16
⇒ x2 + y2 – 8x + 16 – x2 + 2x – 1 – y2 = 16
⇒ – 6x + 15 = 16
⇒ 6x + 1 = 0
The locus of the point is a straight line.
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