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

Options

A. x+y=2
B. `x^(2)+y^(2)=1`
C. `x^(2)+y^(2)=2`
D. `x+y=1`

Answer

C

Explanation

As, we have to find the locus of mid-point of chord and we know that perpendicular from centre bisects the chord.

`thereforeangleOAC=45^(@)` or `(OC)/(OA)=sin45^(@)`
`impliesOC=(2)/(sqrt(2))`
`thereforesqrt(h^(2)+k^(2))=OC`
or `x^(2)+y^(2)=2` is required equation of locus of mid-point of chord subtending right angle at centre.