Number of possible straight lines , passing through (2, 3) and forming a triangle with coordinate ax

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9.Straight Line

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

A

$1$

B

$2$

C

$3$

D

$4$

Solution

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.

Standard 11

Mathematics

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