Question

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`

Answer 1

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.