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Question

The locus of the midpoints of a chord of a circle x2+y2=4, which subtends a right angle at the origin, is

A
x+y=2
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B
x2+y2=1
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C
x2+y2=2
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D
x+y=1
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Solution

The correct option is C x2+y2=2
Let mid point be P(h,k)
and origin be O(0,0) which is also centre of the given circle.
Since chord making right angle at origin and P is mid point, OP will bisect the right angle.
OP =rcos450 where r is radius of the given circle.
OP=(h0)2+(k0)2=2×12=2
Squaring we get, h2+k2=2
Hence locus of P(h,k) is, x2+y2=2

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