Correct Answer - 3
Chord with midpoint (h,k) is
`hx+ky=h^(2)+k^(2)` (1)
Chord of contact of `(x_(1),y_(1))` is
`x x_(1)+y y_(1)=2` (2)
Comparing (1) and (2), we get
`x_(1)=(2h)/(h^(2)+k^(2))` and `y_(1)=(2k)/(h^(2)+k^(2))`
Since `(x_(1),y_(1))` lies on `3x+4y=10,6h+8k=10(h^(2)+k^(2))`.
Therefore, the locus of (h,k) is
`x^(2)+y^(2)-(3)/(5)x-(4)/(5)y=0`
which is a circle with center `P(3//10,4//10)`.Therefore, `OP = 1//2`