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P is the point on the parabola y² = 4x at which the abscissa and ordinate are equal. Find the equation of the circle that passes through the focus of the parabola and touches the parabola at P.

1. x² + y² - 13x + 2y + 12 = 0
2. x² + y² - 3x - 18y + 2 = 0
3. x² + y² + 13x - 2y - 14 = 0
4. x² + y² - x = 0

Correct answer: x² + y² - 13x + 2y + 12 = 0

Solution

P = (4,4); the correct circle must pass through both (4,4) and the focus (1,0), and option 1 satisfies both while matching the tangency condition.

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