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 Incoming links: Power maps of a reciprocal-coordinate hyperbola

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 11 / c / Solution 2026-10-18

From

X = s^{2} - 4

and

Y = 4 s

, elimination of

s

gives

Re v = \frac{( Im v ) ^{2}}{16} - 4, - 15 \leq Im v \leq 15.

This makes the real part a quadratic function of the imaginary part. There is no sign ambiguity because

Y

determines

s = Y /4

uniquely. The calculation illustrates power maps of a reciprocal-coordinate hyperbola.

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