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**bigmansouf** Question: Given that ax+ 3y + 2 = 0 and 2x - by - 5 = 0 are perpendicular lines, find the ratio a:b.

My attempt:

$ax + 3y + 2 = 0 $

$y = -\frac{2}{3} - \frac{a}{3}x$

$2x - by - 5= 0 $

$y = \frac{2}{b}x - \frac{5}{b}$

$ m X - \frac{1}{m} =-1 $

therefore

$-\frac{a}{3} = -\frac{2}{b}.......(1)$

$ m = -\frac{a}{3}$

thus $ -\frac{1}{m} = -\frac{1}{-\frac{a}{3}} = \frac{3}{a}$

$\frac{3}{a}= \frac{2}{b}......(2)$

using simultaneous equation for 1 and 2

you get $a = \pm 3$

and

$b = \pm 2$

therefore the ratio i got is 3:2 or -3:-2

the problem is that the book only states 3:2

in the case of this question i check both positive and negative and my answrs are right but the book only states 3:2 is that just a mistake in the book?

or did my method allowed an extraneous result?