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The tangent to the rectangular hyperbola xy = c² at a point P cuts the x-axis at T and the y-axis at T'. The normal at P cuts the x-axis at N and the y-axis at N'. Let the areas of triangles PNT and PN'T' be D and D'. Find 1/D + 1/D'.

1. equal to a constant independent of P (depends only on c)
2. depends on the parameter t of P
3. equal to 1 regardless of c
4. equal to 2 regardless of c

Correct answer: depends on the parameter t of P

Solution

Working out the intercepts and areas shows 1/D + 1/D' retains dependence on the parameter t of P, so it is not a universal constant.

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