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  • A stick of length 10 units rests against the floor & a wall of a room. If the stick begins to slide on the floor then the locus of its middle point is :Optio

A stick of length 10 units rests against the floor & a wall of a room. If the stick begins to slide on the floor then the locus of its middle point is :

Option: 1

\mathrm{x^{2}+y^{2}=2.5}


Option: 2

\mathrm{x^{2}+y^{2}=25}


Option: 3

\mathrm{x^{2}+y^{2}=100}


Option: 4

none


Answers (1)

best_answer

\mathrm{given \: \left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)=100} \quad \cdots(1)

\mathrm{\mathrm{p}(\mathrm{h}, \mathrm{k})} be the middle \mathrm{pt} then

\mathrm{ \mathrm{h}=\mathrm{a} / 2, \quad \mathrm{k}=\mathrm{b} / 2}
\mathrm{\Rightarrow \quad \mathrm{a}=2 \mathrm{~h} \mathrm{~b}=2 \mathrm{k} }

\mathrm{\text { from (1) } 4 \mathrm{~h}^{2}+4 \mathrm{k}^{2}=100} 
                    \mathrm{\mathrm{~h}^{2}+\mathrm{k}^{2}=25}
                  \mathrm{\text { locus } \mathrm{x}^{2}+\mathrm{y}^{2}=25}

Posted by

Ajit Kumar Dubey

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