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Question

Find the ratio in which the line 3x + 4y + 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0 [NCERT EXEMPLAR]

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Solution

Here, in all equations the coefficient of x is same.
It means all the lines have same slope
So, all the lines are parallel.
Now, the distance between the line 3x + 4y + 2 = 0 and 3x + 4y + 5 = 0 is given by
2-532+42=325=35
Again, the distance between the line 3x + 4y + 2 = 0 and 3x + 4y − 5 = 0 is given by
2+532+42=725=75
Hence, the ratio is given by
35 : 75=3 : 7

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