First slide

Equation of line in Straight lines

Question

The equation of the straight line which passes through the point $(- 4, 3)$ such that the portion of the line between the axes is divided internally by the point in the ratio 5:3 is

Moderate

A

$9 x - 20 y + 96 = 0$
B

$9 x + 20 y = 24$
C

$20 x + 9 y + 53 = 0$
D

None of these

Solution

Let the cuts the axes at points $A (a, 0)$ and $B (0, b) .$ Now, given that $(- 4, 3)$ divides AB in the ratio 5:3. Then, $- 4 = 3 a / 8$ and $3 = 5 b / 8 .$ Therefore $a = - 32 / 3$ and $b = 24 / 5$ . Then using the intercept form $x / a + y / b = 1,$ the equation of line is
$- \frac{3 x}{32} + \frac{5 y}{24} = 1$
or $9 x - 20 y + 96 = 0$

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