 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/11/c/ii/solution

For the real positive dilation factor,

\overset{z}{ˉ} = α \overset{w}{ˉ}

and

z \overset{z}{ˉ} = α^{2} w \overset{w}{ˉ}

. Thus

a α^{2} w \overset{w}{ˉ} + α b \overset{w}{ˉ} + α \overset{ˉ}{b} w + c = 0,

and

A = a α^{2}, B = α b, C = c .

The original PDF specifies a dilation; the differently named transformation in the OCR is an error.

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