one end of the chord is (h,k) itself and the other one will also be lying in the circle, there fore will be satisfying x²+y²=a².

now the mid point is {(h+m)/2 , (k+n)/2}.

where m and n are points on circle..

 

now,let mid point of chord=(x,y)

so,

x=(h+m)/2

=> m=2x-h-----------------(1)

and simillarly n=2y-k-----(2)

now, as m²+n²=a²

so, the locus is...

(2x-h)²+(2y-k)²=a²-------------solve and u'll get the required locus...