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2015-04-23T09:50:04+05:30

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Let the equation of required line in intercept form be \frac{x}{a}+\frac{y}{b}=1

Since the line apsses through point (3,4) :
 \frac{3}{a}+\frac{4}{b}=1

Also area of triangle formed with axes must be 24 :
\frac{1}{2}ab=24\implies b=\frac{48}{a}

Plug this value in earlier equation  and get
 \frac{3}{a}+\frac{4}{48/a}=1
 \frac{3}{a}+\frac{a}{12}=1
 a^2+36=12a
 a^2-12a+36=0
 (a-6)^2=0
 a=6
 \therefore\,b=\frac{48}{a}=\frac{48}{6}=8

Thus the equation of straight line is \frac{x}{6}+\frac{y}{8}=1
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