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Question

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

A
x2+y2=2.5
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B
x2+y2=25
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C
x2+y2=100
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D
none
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Solution

The correct option is D x2+y2=25
Let mid point of Rod be (h,k)
then coordinates of A and B
A(0,2k) B(2h,0)
Distance from A to BAB= fixed (i.e length of rad is fixed)
(2k)2+(2h)2=10
4(k2+h2)=100
k2+h2=25
expressing it in a form of locus x2+y2=25

1419401_1082132_ans_3b1cda7de5844c11b5693d3236c7a172.png

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