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

Straight Lines

Solution:

Let line be $y - 3 = m (x - 2)$
$y$ intercept is $(3 - 2m), x$ intercept is $(2 - \frac{3}{m})$
Area $ = 12$
$\therefore 12 = \frac{1}{2} | 2 - \frac{3}{m}||3 - 2m|$
$\Rightarrow 12 - \frac{9}{m} - 4m = 24$
$\therefore 4m^2 + 12m + 9 = 0$
$\Rightarrow m = -3/2$
or $ 12 - \frac{9}{m} - 4m = -24$
$\Rightarrow 4m^2 - 36 m + 9 =0$
$D > 0$
$\Rightarrow $ There are two values of $m$.
Hence, total $3$ values of $m$.