Mathematics - Straight Lines Question with Solution | TestHub

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