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The line x + y = 1 is tangent to which of the following parabolas?

1. x² - x + y = 0
2. x² + 4y = 0
3. 4x² - 3x + y = 0
4. x² - 2x + 2y = 0

Correct answer: x² - x + y = 0

Solution

Substituting y = 1 - x into x² - x + y = 0 gives x² - 2x + 1 = 0, a perfect square (discriminant 0), so the line touches it.

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