Chapter 16.1, Problem 12PS

To determine

To find: Thepossible values of $b$ .

Answer to Problem 12PS

The possible values of $b$ are $1.5\text{or}2.1$ .

Explanation of Solution

Given information:

The given equation is,

  $2x+by+3=0$

The possible values of $b$ are calculated as,

  $\begin{array}{l}d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}\\ 6=\frac{\left|2\left(3\right)+b\left(4\right)+3\right|}{\sqrt{{\left(2\right)}^2+{\left(b\right)}^2}}\\ 36\left(4+b^2\right)={\left(9+4b\right)}^2\\ b=1.5\text{or}2.1\end{array}$

Thus, the possible values of $b$ are $1.5\text{or}2.1$ .