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  • Two points A and B move on the x –axis and the y – axis respectively such that the distance between the two points is always same. The locus of middle point of AB is  </p

Two points A and B move on the x –axis and the y – axis respectively such that the distance between the two points is always same. The locus of middle point of AB is

 

Option: 1

a straight line


Option: 2

a circle


Option: 3

a parabola


Option: 4

an ellipse


Answers (1)

best_answer

Given \mathrm{a}^{2}+\mathrm{b}^{2}=\mathrm{P}^{2} \quad  (p is constant)


\mathrm{\mathrm{h}=\frac{\mathrm{a}}{2}, \mathrm{k}=\frac{\mathrm{b}}{2}}

\mathrm{Hence \, 4 h^{2}+4 k^{2}=P^{2}}
\mathrm{\Rightarrow \mathrm{x}^{2}+\mathrm{y}^{2}=\frac{\mathrm{P}^{2}}{4}}

Hence (B) is the correct answer.

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