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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
Options
9x − 20y + 96 = 0
9x + 20y = 24
20x + 9y + 53 = 0
none of these
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Solution
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:
\[\frac{x}{\frac{- 32}{3}} + \frac{y}{\frac{24}{5}} = 1\]
\[ \Rightarrow \frac{- 3x}{32} + \frac{5y}{24} = 1\]
\[ \Rightarrow - 9x + 20y = 96\]
\[ \Rightarrow 9x - 20y + 96 = 0\]
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