Question

The ends of a rod of length l move on two mutually perpendicular lines. The locus of the point on the rod which divides it in the ratio 1 : 2 is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

According to the figure

$P(h,k)dividesABintheratio1:2\Rightarrow (\frac{2a}{3},\frac{b}{3})=(h,k)a=\frac{3h}{2},b=3k{a}^2+b^2=l^2\Rightarrow \frac{9h^2}{4}+9k^2=l^2\Rightarrow 9h^2+36k^2=4l^2\therefore locusofPIS9x^2+36y^2=4l^2$