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 5:3is

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

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