Question

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point (13, 32). The line K is parallel to L and has the equation $\frac{x}{e}+\frac{y}{3}=1$. Then the distance between L and K is

• A. $\frac{23}{\sqrt{15}}$
• B. $\sqrt{17}$
• C. $\frac{17}{\sqrt{15}}$
• D. $\frac{23}{\sqrt{17}}$

Answer 1

The correct option is D $\frac{23}{\sqrt{17}}$

As line L is passing through $(13,32)$

So, $\frac{13}{5}+\frac{32}{b}=1$

$\Rightarrow \frac{32}{b}=\frac{-8}{5}$

$\therefore b=-20$

Line K is parallel to line L equation of:-

$\frac{x}{5}-\frac{y}{20}=a$

or

$\frac{x}{5a}-\frac{y}{20a}=1$

Comparing with $\frac{x}{c}+\frac{y}{3}=1$

$20a=-3$ $\Rightarrow a=-3/20$

$c=5a$ $\Rightarrow c=-3/4$

Distance between the lines is,

$\frac{|1-a|}{\sqrt{\frac{1}{25}+\frac{1}{400}}}=\frac{|\frac{-3}{20}-1|}{\sqrt{\frac{17}{400}}}=\frac{23}{\sqrt{17}}$.