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

with the help of the fig. area of {\Delta} \mathrm{OAB}= \pm 12
\mathrm{ie. \quad \frac{1}{2}\left(\frac{2 m-3}{m}\right)(3-2 m)= \pm 12}

taking + sign me get \mathrm{(2 m+3)^{2}=0}
this gives one value of \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}

\mathrm{\Rightarrow \quad 3} st. lines are possible.

Posted by

Rishabh

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