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Question
If the straight lines 12y = − (p + 3)x + 12, 12x – 7y = 16 are perpendicular then find ‘p’
Solution
Slope of the first line 12y = − (p + 3)x + 12
y = `(-("p" + 3)x)/12` + 1 ...(Comparing with y = mx + c)
Slope of the second line (m1) = `(-("p" + 3))/12`
Slope of the second line 12x – 7y = 16
(m2) = `(-"a")/"b" = (-12)/(-7) =12/7`
Since the two lines are perpendicular
m1 × m2 = − 1
`(-("p" + 3))/12 xx 12/7` = − 1
⇒ `(-("p" + 3))/7` = − 1
− (p + 3) = − 7
– p – 3 = − 7
⇒ − p = − 7 + 3
− p = − 4
⇒ p = 4
The value of p = 4
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