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Question
Find the equation of a line passing through the intersection of x + 2y + 1= 0 and 2x - 3y = 12 and perpendicular to the line 2x + 3y = 9
Solution
x + 2y + 1 = 0.............(1)
2x - 3y = 12...........(2)
(1) can be written as 2x + 4y = -2....(3)
(2) can be rewritten as 2x - 3y = 12........(4)
subtracting (4) from (3) we get
y = -2
x = 3
i.e (3,-2)
Point of intersection of (1) and (2) is (3,-2)
Slope of 2x + 3y = 9 is `(-2)/3`
Slope of required line is `3/2`
equation of required lineis `("y" - "y"_1)/("x" - "x"_1)` = m
`("y" + 2)/("x" - 3) = 2/3`
⇒ #x - 9 = 2y + 4
⇒ 3x - 2y = 13
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