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Home / Aptitude Tests / Further Mathematics / Given that \(3x + 4y...
Given that 3x+4y+6=0 and 4xby+3=0 are p...

Given that 3x+4y+6=0 and 4xby+3=0 are perpendicular, find the value of b.

A.

4

B.

3

C.

13

D.

14

Correct answer is B

When you have two lines, y1,y2, perpendicular to each other, the product of their slopes = -1.

3x+4y+6=04y=63x

\frac{\mathrm d y}{\mathrm d x} = \frac{-3}{4}

Also, 4x - by + 3 = 0  \implies by = 4x + 3

y = \frac{4}{b}x + \frac{3}{b} 

\frac{\mathrm d y}{\mathrm d x} = \frac{4}{b}

\frac{-3}{4} \times \frac{4}{b} = -1 \implies \frac{4}{b} = \frac{4}{3}

b = 3