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Explanation

Given, circle is `x^(2)+y^(2)=r^(2)`
Equation of chord whose mid point is given, is
` T = S_(1) rArr xx_(1)-r^(2)=x_(1)^(2)+y_(1)^(2)-r^(2)`
It also passes through (h, k)`hx_(1)+ky_(1)=x_(1)^(2)+y_(1)^(2)`
`therefore` Locus of `(x_(1), y_(1))` is

`x^(2)+y^(2)=hx + ky`
Alternate Solution
Let M be the mid-point of chord AB.
`rArr CMcot MP`
`rArr ("slope of CM")* ("slope of MP")=-1`
`rArr (y_(1))/(x_(1))*(k-y_(1))/(h-x_(1))=-1`
`rArr ky_(1)-h_(1)^(2)=-hx_(1)+x_(1)^(2)`
Hence, required locus is `x^(2)+y^(2)=hx + ky`