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Question

The equation of the line, when the portion of it intercepted between the axes is divided by the point $$(2,3)$$ in the ratio of $$3:2$$, is


A
Either x+y=4 or 9x+y=12
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B
Either x+y=5 or 4x+9y=30
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C
Either x+y=4 or x+9y=12
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D
Either x+y=5 or 9x+4y=30
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Solution

The correct option is D Either $$x+y = 5$$ or $$4x+9y=30$$
Now $$\dfrac{2a}{5}=2 \Rightarrow a=5$$

$$\dfrac{3b}{5}=3 \Rightarrow b=5$$ 

Therefore equation of the line is $$\dfrac{x}{5}+\dfrac{y}{5}=1 \Rightarrow x+y=5$$.

Now $$\dfrac{3a}{5}=2 \Rightarrow a=\dfrac{10}{3}$$

$$\dfrac{2b}{5}=3 \Rightarrow b=\dfrac{15}{2}$$

Therefore equation of the line is $$\dfrac{x}{10/3}+\dfrac{y}{15/2}=1$$.

$$\Rightarrow \dfrac{3x}{10}+\dfrac{2y}{15}=1$$

$$\Rightarrow 9x+4y=30$$ 

Hence the equation of the line is $$x+y=5$$ or $$9x+4y=30$$.


855005_926197_ans_1f69b996ee544942b7dbab2ba479f442.png

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