Question

The ends of the rod of length 'L' move on the coordinate axes. The locus of point rod which divides it in the ratio 1:2 is

• A. $9x^2+36y^2=144$
• B. $9x^2+36y^2=l$
• C. $36x^2+9y^2=l$
• D. $9x^2+36y^2=4l^2$

Answer 1

The correct option is D $9x^2+36y^2=4l^2$

Let co-ordinate point be $(x_1,y_1)$ & coordinates of ends of rod be $(x,0)$ & $(0,y)$

such that

$x^2+y^2=l^2$ ………..$\left(1\right)$

From the ratio we know that:-

$x_1=2x/3$

$\Rightarrow x=3x_1/2$ ……..$\left(2\right)$

$y_1=y/3$

$\Rightarrow y=3y_1$ …………$\left(3\right)$

Sub $\left(2\right)$ & $\left(3\right)$ in $\left(1\right)$

$\frac{9x_1^2}{4}+9y_1^2=l^2$

$9x_1^2+36y_1^2=4l^2$

Locus would be (sub $x_1=x$ & $y_1=y$)

$9x^2+36y^2=4l^2$.