question_answer

A rod of length 7 is kept with the support of a wall and floor of a room. If rod starts slipping, then the locus of its midpoint is

A)  a straight line    

B)  a circle

C)  a parabola        

D)  an ellipse

Correct Answer: B

Solution :

 Let coordinates of both the extremes of the rod be (a,0) and (0,b). Coordinates of mid point are \[\left( \frac{a}{2},\frac{b}{2} \right)\] \[\therefore \] \[h=\frac{a}{2},k=\frac{b}{2}\] But  \[{{a}^{2}}+{{b}^{2}}={{l}^{2}}\] \[\Rightarrow \] \[4{{h}^{2}}+4{{k}^{2}}={{l}^{2}}\] \[\Rightarrow \] \[{{h}^{2}}+{{k}^{2}}=\frac{{{l}^{2}}}{4}\] Hence, locus of mid point is \[{{x}^{2}}+{{y}^{2}}=\frac{{{l}^{2}}}{4}\] which is the equation of circle.