Question

The distance between 5x – 3y – 4 = 0 and 10x – 6y – 9 = 0 is with solution




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Answer 1

The given lines are

5x - 3y - 4 = 0 .....(1)

10x - 6y - 9 = 0

or, 5x - 3y - 9/2 = 0 ....(2)

We see that the lines (1) and (2) are parallel to each other.

• Formula to find the distance between the two parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0:
• If d be the distance between them, then
• d = | c₁ - c₂ | / √(a² + b²) units

From equation (1) and (2), we get:

a = 5, b = - 3 and c₁ = - 4, c₂ = - 9/2

Therefore the required distance is

= | - 4 - (- 9/2) | / √{5² + (- 3)²} units

= | - 4 + 9/2 | / √(25 + 9) units

= | 1/2 | / √34 units

= (1/2) / √34 units

= 1 / (2√34) units