Coordinate Geometry Question 17
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
[IIT 1987; RPET 1997]
Options:
A) $ 36x^{2}+9y^{2}=4l^{2} $
B) $ 36x^{2}+9y^{2}=l^{2} $
C) $ 9x^{2}+36y^{2}=4l^{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
According to the figure $ AP:PB=1:2, $ then $ h=\frac{1\times 0+2\times a}{1+2}=\frac{2a}{3} $ or $ a=\frac{3h}{2}, $ similarly $ b=3k $ Now we have $ OA^{2}+OB^{2}=AB^{2} $
$ \Rightarrow {{( \frac{3h}{2} )}^{2}}+{{(3k)}^{2}}=l^{2} $
Hence locus of $ P(h,k) $ is given by $ 9x^{2}+36y^{2}=4l^{2} $ .
BETA
