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A hyperbola with foci at (+-2, 0) passes through the point P(sqrt2, sqrt3). The tangent to this hyperbola at P also passes through which of the following points?

1. (-sqrt2, -sqrt3)
2. (3*sqrt2, 2*sqrt3)
3. (2*sqrt2, 3*sqrt3)
4. (sqrt3, sqrt2)

Correct answer: (2*sqrt2, 3*sqrt3)

Solution

Solving gives a² = 1, b² = 3, hyperbola x² - y²/3 = 1; the tangent at P is sqrt2*x - sqrt3*y/3 = 1, which the point (2sqrt2, 3sqrt3) satisfies.

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