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Problem 6 - Entrance Test

The circle x²+y²–4x–6y+k=0 touches the x–axis. Find k.

Correct: A

Rewrite: (x–2)²+(y–3)²=13–k. Center (2,3), radius √(13–k). Touches x–axis means radius equals y–coordinate of center, so √(13–k)=3 → 13–k=9 → k=4.