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.You need to login to perform this action.
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