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The circle S: x² + y² + k*x + (k+1)*y - (k+1) = 0 passes through two fixed points for all real values of k. If the minimum radius of circle S is 1/sqrt(P), find the value of P.

1. 4
2. 6
3. 8
4. 16

Correct answer: 8

Solution

The fixed points are (1/2, 1/2) and (1, 0). Expressing radius² as a function of k gives r² = (2k²+6k+5)/4, minimized at k = -3/2, yielding r_min² = 1/8, so r_min = 1/sqrt(8) and P = 8.

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