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A line passes through the point $(3,4)$ and cuts off intercepts from the coordinates axes such that their sum is 14. The equation of the line is
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Verified Answer
The correct answer is:
$4 x+3 y=24$
Given $a+b=14 \Rightarrow a=14-b$
Hence the equation of straight line is $\frac{x}{14-b}+\frac{y}{b}=1$.
Also, it passes through $(3,4)$
$\therefore \frac{3}{14-b}+\frac{4}{b}=1 \Rightarrow b=8$
or 7
Therefore equations are $4 x+3 y=24$ and $x+y=7$.
Trick : This question can be checked with the options as the line $4 x+3 y=24$ passes through $(3,4)$ and also cuts the intercepts from the axes whose sum is 14 .
Hence the equation of straight line is $\frac{x}{14-b}+\frac{y}{b}=1$.
Also, it passes through $(3,4)$
$\therefore \frac{3}{14-b}+\frac{4}{b}=1 \Rightarrow b=8$
or 7
Therefore equations are $4 x+3 y=24$ and $x+y=7$.
Trick : This question can be checked with the options as the line $4 x+3 y=24$ passes through $(3,4)$ and also cuts the intercepts from the axes whose sum is 14 .
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