 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/2/a/solution

At an intersection,

x^{2} = (x - 1)^{2} = x^{2} - 2 x + 1

, so

x = 1/2

. Substitution into either parabola gives

(x, y) = (\frac{1}{2}, \frac{1}{4}) .

The resulting linear equation for

x

has only one solution, so this is the unique intersection.

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