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  • Consider the straight line where <img alt="\mathrm{a, b, c\: and \: R

Consider the straight line \mathrm{a x+b y=c} where \mathrm{a, b, c\: and \: R }. This line meets the coordinate axes at \mathrm{' P ' and\: ' Q ' }respectively. If the area of triangle \mathrm{O P Q, ' O '} being origin, does not depend upon \mathrm{ a, b \, and\: c}, then -
 

Option: 1

\mathrm{\text[ a, b, c are \: in\: G.P.]}


 


Option: 2

\mathrm{a, c, b \: are \: in \: G.P.}
 


Option: 3

\mathrm{a, b, c\: \: are \: in \: \: A.P.}
 


Option: 4

\mathrm{a, c, b \: are\: in\: A.P.}


Answers (1)

best_answer

\mathrm{\mathrm{P} \equiv\left(\frac{c}{a}, 0\right), \mathrm{Q} \equiv\left(0, \frac{c}{b}\right) }

\mathrm{\triangle \mathrm{OPQ}=\frac{1}{2}(\mathrm{OP})(\mathrm{OQ})=\frac{1}{2} \frac{c^2}{a b} } clearly \mathrm{\triangle \mathrm{OPQ} } will not depend upon \mathrm{\mathrm{a}, \mathrm{b}\: and \: \mathrm{c} }  if  \mathrm{\mathrm{c} 2=\mathrm{ab},}

\mathrm{i.e. a, c, b \: are \: in \: G.P.}

Hence option 2 is correct.
 

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Riya

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