Find the vertices of the two right angled triangles each having area $18$ and such that the point $(2,4)$ lies on the hypotenuse and the other two sides are formed by the $x$ and $y$ axes.
Since, the triangle is formed by the $x$ and $y$ axes, the product of the intercepts is $36$.
So,we have to find $2$ lines which has product of intercepts equal to $36$ and which passes through $(2,4)$.From here, I can solve the problem by trial and error,but I want to do this sum without any trial-error method.
So, I form $2$ equations of line with it. But, I cannot proceed any further. Please help!