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The tangent to the hyperbola x² - 3y² = 3 at the vertex (sqrt 3, 0), together with the two asymptotes, encloses a triangle. Which description is correct?

1. a triangle whose area is sqrt 3 square units
2. an equilateral triangle
3. an isosceles triangle which is not equilateral
4. a right isosceles triangle

Correct answer: a triangle whose area is sqrt 3 square units

Solution

The triangle has vertices (0,0), (sqrt3, 1), (sqrt3, -1); base 2 and height sqrt3 give area sqrt 3 square units.

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