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When the circle defined by x² + y² = 1 intersects the rectangular hyperbola xy = 1 at four points (x_i, y_i) for i = 1, 2, 3, 4, which of the following is true?

1. The product of x-coordinates, x₁x₂x₃x₄, equals -1.
2. The product of y-coordinates, y₁y₂y₃y₄, equals 1.
3. The sum of x-coordinates, x₁ + x₂ + x₃ + x₄, equals 0.
4. The sum of y-coordinates, y₁ + y₂ + y₃ + y₄, equals 0.

Correct answer: The sum of x-coordinates, x₁ + x₂ + x₃ + x₄, equals 0.

Solution

The sum of x-coordinates of the intersection points of the circle and the rectangular hyperbola is zero because the circle is symmetric about the origin and the hyperbola is symmetric about the line y = x.

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