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

विकल्प

• 9x − 20y + 96 = 0

•  9x + 20y = 24

•  20x + 9y + 53 = 0

• none of these

Answer 1

9x − 20y + 96 = 0

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

\[\therefore - 4 = \frac{5 \times 0 + 3 \times a}{5 + 3} \text { and } 3 = \frac{5 \times b + 3 \times 0}{5 + 3}\]

\[ \Rightarrow a = \frac{- 32}{3} \text { and } b = \frac{24}{5}\]

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

\[\frac{x}{\frac{- 32}{3}} + \frac{y}{\frac{24}{5}} = 1\]

\[ \Rightarrow \frac{- 3x}{32} + \frac{5y}{24} = 1\]

\[ \Rightarrow - 9x + 20y = 96\]

\[ \Rightarrow 9x - 20y + 96 = 0\]