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The locus of the mid point of a chord of...

The locus of the mid point of a chord of the circle `x^2+y^2=4` which subtends a right angle at the origin is

A

`x + y = 2`

B

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

C

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

D

`x+y=1`

Text Solution

Verified by Experts

The correct Answer is:
C
We have to find loucs of mid-point of chord and we know perpendicular from centre bisects the chord.
`therefore angleOAC=45^(@)`

In` DeltaOAC, (OC)/(OA)=sin45^(@)`
`rArr OC=(2)/(sqrt2)=sqrt2`
Also, ` sqrt(h^(2)+k^(2))=OC^(2)`
Hence, `x^(2)+y ^(2)=2` is required equation of locus of mid-point of chord substending right angle at the centre.
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