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Given that the line L1: MX + 8y + n = 0 and L2: 2x + MY-1 = 0 are parallel, and the distance between L1 and L2 is 5, the equation of line L1 is obtained
When m = 4, the equation of line L1 is 4x + 8y + n = 0, and the equation of line L2 is 4x + 8y-2 = 0. The distance between two parallel lines is | n + 2 | 16 + 64 = 5, and the solution is n = - 22, or n = 18. Therefore, the equation of line L1 is 2x + 4y-11 = 0, or 2x + 4Y + 9 = 0. When m = - 4, the equation of line L1 is 4x-8y-n = 0, and the equation of line L2 is written as 4x-8y-2 = 0 The line distance is | n-2 | 16 + 64 = 5. The solution is n = - 18, or n = 22. Therefore, the equation of the line L1 is 2x-4y + 9 = 0, or 2x-4y-11 = 0. In conclusion, the equation of the line L1 is 2x + 4y-11 = 0, or 2x + 4Y + 9 = 0, or 2x-4y + 9 = 0, or 2x-4y-11 = 0
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