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For the parabola S: y² = 2x, the tangent at P(2, 2) meets the x-axis at Q, and the normal at P meets the parabola again at R. Find the area (in square units) of triangle PQR.

1. 25/2
2. 35/2
3. 15/2
4. 25

Correct answer: 25/2

Solution

P corresponds to parameter t1 = 2 (since point is (a t², 2a t) with a = 1/2 gives (t²/2, t)). Working out Q and R coordinates and the area gives 25/2.

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