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The locus of the midpoint of a chord of the circle `x^2+y^2=4` which subtends a right angle at the origins is (a) `x+y=2` (b) `x^2+y^2=1` `x^2+y^2=2` (d) `x+y=1`

A

`x^(2)+y^(2)-2x+y-2=0`

B

`x^(2)+y^(2)-2x-y-2=0`

C

`x^(2)+y^(2)-2x+y+1=0`

D

`x^(2)+y^(2)-2x+y+2=0`

Text Solution

Verified by Experts

The correct Answer is:
D

`AP=PC`
`AP^(2)=PC^(2)`
`AP^(2)=(h-2)^(2)+(k+1)^(2)`
`(1)^(2)-(h^(2)+k^(2))=h^(2)+k^(2)-4h+2k+5`
`implies2x^(2)+2y^(2)-4x+2y+4=0`
`x^(2)+y^(2)-2x+y+2=0`
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