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Question
If the straight lines 3x – 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another, find the value of a.
Solution
3x - 5y = 7
`=> 5y = 3x - 7`
`=> y = 3/5 x - 7/5`
⇒ Its slope = `3/5`
4x + ay + 9 = 0
⇒ ay = -4x - 9
`=> y = (-4)/a x - 9/a`
⇒ Its slope = `(-4)/a`
Since lines are perpendicular to each other,
`3/5 xx (-4)/a = -1 => 3/5 xx 4/a = 1 => 4/a = 5/3`
`=> a = (4xx3)/5 = 12/5`
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