 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/5/a/solution

Substituting the line into the hyperbola gives

7 x^{2} - (x + 1)^{2} = 7 ⟺ 3 x^{2} - x - 4 = (3 x - 4) (x + 1) = 0.

The two polynomial roots give all intersections:

(x, y) = (- 1, 0), (4/3, 7/3) .

Both satisfy the original line as well as the curve.

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