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  • The number of possible straight lines , passing through and forming a triangle with coordinate axes, whose area

The number of possible straight lines , passing through (2,3) and forming a triangle with coordinate axes, whose area is 12 sq. units, is

Option: 1

one


Option: 2

two


Option: 3

three


Option: 4

four


Answers (1)

best_answer

equation of any line through (2,3) is \mathrm{y}-3=\mathrm{m}(\mathrm{x}-2)

\mathrm{\mathrm{y}=\mathrm{mx}-2 \mathrm{~m}+3}

with the help of the fig. area of \mathrm{{ }_{\Delta} \mathrm{OAB}= \pm 12}

\mathrm{ie. \: \frac{1}{2}\left(\frac{2 m-3}{m}\right)(3-2 m)= \pm 12}
\mathrm{taking + sign\: me\: get (2 m+3)^{2}=0}
this gives one value of \mathrm{\mathrm{m}=-3 / 2}

taking negative sign we get
\mathrm{4 m^{2}-36 m+9=0 \quad(D>0)}

quadratic in \mathrm{m} gives 2 values of \mathrm{m}
\Rightarrow \: 3 st. lines are possible.

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Sayak

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