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

Answer 1

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