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 

A. 9x – 20y + 96 = 0

 B. 9x + 20y = 24 

C. 20x + 9y + 53 = 0 

D. none of these

Answer 1

Let the required line intersects the coordinate axis at (a, 0) and (0, b).

The point (− 4, 3) divides the required line in the ratio 5 : 3

∴ -4 = \(\frac{5\times0+3\times a}{5+3}\)  and 3 = \(\frac{5\times b+3\times 0}{5+3}\) 

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

Hence, the equation of the required line is given below:

\(\frac{x}{-\frac{32}{3}}\) + \(\frac{y}{-\frac{32}{3}}\)

 \(-\frac{3x}{32}\) + \(\frac{5y}{24}\) = 1

⇒ -9x + 20y = 96 

⇒ 9x – 20y + 96 = 0