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Question
Choose correct alternatives:
If distance between lines (x - 2y)2 + k(x - 2y) = 0 is 3 units, then k = ______.
Options
± 3
± 5`sqrt5`
0
`±3sqrt5`
Solution
If distance between lines (x - 2y)2 + k(x - 2y) = 0 is 3 units, then k = `±3sqrt5`
Explanation:
(x - 2y)2 + k(x - 2y) = 0
∴ (x - 2y)(x - 2y + k) = 0
∴ equations of the lines are x - 2y = 0 and x - 2y + k = 0 which are parallel to each other.
∴ `|("k" - 0)/(sqrt(1 + 4))| = 3`
∴ k = `±3sqrt5`
Notes
The answer in the textbook is incorrect.
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