Find the equation of the line which passes through the point (-4, 3) a

1.	Find the equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by this point.
Answer» The equation of the line with intercepts a and b is x/a + y/b = 1 Given: The line \(\frac{x}{a}+\frac{y}{b}=1\) intersects the axes (a,0) and (0,b). Explanation: So, (-4,3) divides the line segment AB and the ratio 5:3 -4 = \(\frac{5+3a}{5+3},3=\frac{5b}{5+3}=1\) ⇒ a = \(-\frac{32}{3},b=\frac{24}{5}\) So, the equation of the line is \(\frac{x}{\frac{32}{5}}+\frac{y}{\frac{24}{5}}=1\) ⇒ 9x – 20y = -96 Hence, the equation of line is 9x – 20y = -96

Find the equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5: 3 by this point.

Answer»

The equation of the line with intercepts a and b is x/a + y/b = 1

Given:

The line \(\frac{x}{a}+\frac{y}{b}=1\) intersects the axes (a,0) and (0,b).

Explanation:

So, (-4,3) divides the line segment AB and the ratio 5:3

-4 = \(\frac{5+3a}{5+3},3=\frac{5b}{5+3}=1\)

⇒ a = \(-\frac{32}{3},b=\frac{24}{5}\)

So, the equation of the line is \(\frac{x}{\frac{32}{5}}+\frac{y}{\frac{24}{5}}=1\)

⇒ 9x – 20y = -96

Hence, the equation of line is 9x – 20y = -96