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प्रश्न
Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 0
उत्तर
2x + 5y = 7 and 12x + 5y + 7 = 0
The equation of the given lines are
12x + 5y – 7 = 0 ......(1)
12x + 5y + 7 = 0 .......(2)
The distance between the parallel lines
ax + by + c1 = 0 and ax + by + c2 = 0 is
The equation of any line parallel to (1) is
d = `("c"_1 + "c"_2)/sqrt("a"^2 + "b"^2)`
∴ The required distance - `(- 7 - 7)/sqrt(12^2 + 5^2)`
= `(-14)/sqrt(144 + 25)`
= `- 14/sqrt(169)`
= `- 14/13`
The distance cannot be negative
∴ Required distance = `14/13`
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