Find The Locus Of Middle Points Of Chords Of The Circle x2 + y2 = a2, Which Subtend Right Angle At The Point (c, 0).

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Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0).


Correct option is

2(x2 + y2) – 2cx + c2 – a2 = 0


Let N (hk) be the middle point of any chord AB, which subtend a right angle at P(c, 0).


(since distance of the vertices from middle point of the hypotenuse are equal)



∴ Locus of N(hk) is  

             2(x2 + y2) – 2cx + c2 – a2 = 0





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