The locus of the mid point of a chord of the circle x2 + y2 = 4 which subtends a right angle at the

Question

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

Accepted Answer

We have to find locus of mid point of chord and we know perpendicular from centre bisects the chord.
∴ ∠OAC = 45^o
In ᐃOAC,

= sin 45^o ⇒ OC =

Also,

= OC² Hence, x² + y² = 2 is required equation of locus of locus of mid point of chord subtending right angle at the centre.

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