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If the line 2x - y + 1 = 0 serves as a tangent to the hyperbola x²/a² - y²/16 = 1, which of these sets of values cannot represent the sides of a right triangle?

1. a, 4, 2
2. 2a, 4, 1
3. 2a, 4, 1
4. 2a, 8, 1

Correct answer: 2a, 8, 1

Solution

The equation of the tangent line to the hyperbola and the equation of the hyperbola itself must be related in such a way that the values of a, b, and c satisfy the equation c² = a²m² - b², which is not satisfied by the set of values 2a, 8, 1.

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