The number of possible straight lines , passi | vedclass

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Question

equation of any line through $(2, 3)$ is

$y -3 = m(x - 2)$

$y = mx - 2m + 3$

with the help of the fig. area of $\Delta OAB = \pm  1

Vedclass · Accepted Answer

$3$

Vedclass · Answer

equation of any line through $(2, 3)$ is

$y -3 = m(x - 2)$

$y = mx - 2m + 3$

with the help of the fig. area of $\Delta OAB = \pm  12$

ie.    $\frac{1}{2}\left( {\frac{{2m - 3}}{m}} \right)(3 - 2m) =  \pm 12$

taking $+$ sign me get $(2m+3)^2 = 0$

this gives one value of $m = -3/2$

taking negative sign we get

$4m^2 - 36m + 9 = 0\,\,(D > 0)$

quadratic in m gives $2$ values of $m$

$\Rightarrow\,\,3$ st. lines are possible.

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

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