Question

Find number of straight line passing through $(2,4)$ and forming a triangle of $16c{m}^2$ with the coordinate axis.

Answer 1

Let the coordinate axes at the straight line be $(a,0)$ and $(0,b)$.

Therefore, the equation of the straight line is,

$\frac{x}{a}+\frac{y}{b}=1$

It is passing through $(2,4)$. So,

$\frac{2}{a}+\frac{4}{b}=1$

$4a+2b=ab$ ...... (1)

Given:

Area of the triangle formed $=16c{m}^2$

$\frac{1}{2}\times ab=16$

$ab=32$

$b=\frac{32}{a}$

Substitute this value of $b$ in the equation (1).

$4a+\frac{64}{a}=32$

$4a^2+64=32a$

$a^2-8a+16=0$

$a=4$

Therefore,

$b=8$

THus, only one such straight line is possible.