First slide

Equation of line in Straight lines

Question

The line L is 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 $\frac{x}{c} + \frac{y}{3} = 1$ Then the distance between $L$ and $K$ is

Moderate

A

$17 / \sqrt{15}$
B

$23 / \sqrt{17}$
C

$23 / \sqrt{15}$
D

$\sqrt{15}$

Solution

As $L : \frac{x}{5} + \frac{y}{b} = 1$ passes through $(13, 32),$
we get
$\frac{13}{5} + \frac{32}{b} = 1 \Rightarrow b = - 20$
As $K : \frac{x}{c} + \frac{y}{3} = 1$ is parallel to $L$
$- \frac{b}{5} = - \frac{3}{c} \Rightarrow c = - \frac{3}{4}$
Now equation of L and K are respectively
$4 x - y - 20 = 0$ and
$4 x - y + 3 = 0$ and the distance between them is
$\frac{| - 20 - 3 |}{\sqrt{16 + 1}} = \frac{23}{\sqrt{17}}$

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