The line L given by (x)/(5)+(y)/(b)=1 passes through the point...

Slope of line $L=-\frac{b}{5}$ Slope of line $\mathrm{K}=-\frac{3}{\mathrm{c}}$ Line $L$ is parallel to line $k$. \Rightarrow $\frac{\mathrm{b}}{5}=\frac{3}{\mathrm{c}} \quad \Rightarrow \mathrm{bc}=$15 $(13,32)$ is a point on $\mathrm{L}$. $$\begin{aligned}& \Rightarrow \frac{13}{5}+\frac{32}{b}=1 \quad \Rightarrow \frac{32}{b}=-\frac{8}{5}\\ & \Rightarrow \mathrm{b}=-20 \quad \Rightarrow \mathrm{c}=-\frac{3}{4}\\ & \end{aligned}$$Equation$of K: y-4 x=3$ Distance between $\mathrm{L}$ and $\mathrm{K}=\frac{|52-32+3|}{\sqrt{17}}=\frac{23}{\sqrt{17}}