Question

A road of length l slides between the two perpendicular lines . Find the locus of the point the road which divides it in the ratio 1:2 .

Answer 1

Let the road be lying in X and Y axis. Let point Y contact in X axis be $(a,0)$ and that of y be $(0,b)$

Let the point of road be $(h,k)$

As the point divide in the ratio $1:2$ by section formula we have

$h=\frac{a}{3}or,a=3h\to eqn\left(1\right)h=\frac{2b}{3}b=\frac{3h}{2}\to eqn\left(2\right)$

By Pythagorus theorem

$a^2+b^2+c^{2}9h^2+\frac{9h^2}{4}=c^2$

Replace $h,h$ by $x,y$ to get $10cm$