It is known that the line L: x-y-1 = 0 and the circle C: (x-3) square + (y-4) square = 2 are tangent to point P and pass through point P Given that the line L: x-y-1 = 0 and circle C: (x-3) square + (y-4) square = 2 are tangent to point P, the line L1 passing through point P intersects circle C at another point Q, and the length of segment PQ is 2, the L1 equation is solved

Let the coordinates of point p be (x1, Y1), and the coordinates of point Q be (X2, Y2)
From the known x1-y1-1 = 0, (x1-3) ² + (y1-4) ² = 2, the coordinates of P are (4,3). And √ [(x2-4) ² + (y2-3) ²] = 2, (two-point spacing formula), and (x2-3) ² + (y2-4) ² = 2, the coordinates of Q are (2,3) or (4,5),
Then the equation of L1 is y = 3, or x = 4

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