Find the ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0
Given:
Lines A: 3x + 4y + 5 = 0 and B: 3x + 4y – 5 = 0
And also C: 3x + 4y + 2 = 0
To find:
Ratio in which line C divides the distance between the lines A and B
Explanation:
The distance between two parallel line ax + by + c1 = 0 and ax + by + c2 = 0 is
Therefore the distance between two parallel line 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is
The distance between the line 3x + 4y + 2 = 0 and 3x + 4y – 5 = 0 is
Hence, the required ratio