First slide

Equation of line in Straight lines

Question

Let $3, 4$ are the intercepts of a line then intercepts of a line which is perpendicular to the line and passing through the point $(1, 3)$ is

Moderate

A

$3, \frac{4}{9}$
B

$3, - \frac{9}{4}$
C

$- 3, \frac{9}{4}$
D

$- 3, \frac{4}{3}$

Solution

$Equation of the line which makes intercepts a, b in axes is \frac{x}{a} + \frac{y}{b} = 1, its slope is - \frac{b}{a}$
$Hence the slope of the line which makes intercepts 3, 4 on axes is - \frac{4}{3}$
$Since required line is perpendicular to the above line, its slope is \frac{3}{4}$
$Equation of the line passing through (1, 3) and having slope \frac{3}{4} is y - 3 = \frac{3}{4} (x - 1)$
Simplify
$\begin{matrix} 4 y - 12 = 3 x - 3 \\ 3 x - 4 y = - 9 \\ \frac{x}{- 3} + \frac{y}{\frac{9}{4}} = 1 \end{matrix}$
$Therefore, the intercepts are - 3, \frac{9}{4}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App