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Question -

Determine the distance between the following pair of parallel lines:
(i) 4x – 3y – 9 = 0 and 4x – 3y – 24 = 0
(ii) 8x + 15y – 34 = 0 and 8x + 15y + 31 = 0



Answer -

(i) 4x – 3y – 9 = 0 and 4x– 3y – 24 = 0

Given:

The parallel lines are

4x − 3y − 9= 0 … (1)

4x − 3y − 24= 0 … (2)

Let d be the distancebetween the given lines.

So,

The distance betweengivens parallel line is 3units.

(ii) 8x + 15y – 34 = 0 and8x + 15y + 31 = 0

Given:

The parallel lines are

8x +15y − 34 = 0 … (1)

8x + 15y + 31 = 0 …(2)

Let d be the distancebetween the given lines.

So,

The distance betweengivens parallel line is 65/17 units.

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