The Locus Of The Mid Points Of A Chord Of The Circles x2 + y2 = 4, Which Subtends A Right Angle At The Origin Is:

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


Correct option is

x2 + y2 = 2

Equation of the given circle is 

                   x2 + y2 = 4                    …(1) 

Let AB is the chord of the circle which subtends a right angle at the origin and coordinate of A & B are (2, 0) & (0, 2) resp. 

Let (x1y1) is the mid point of the chord AB then   





Locus of the mid point (x1y1) is  

          x2 + y2 = 2.




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