Find the locus of the mid points of the chords of the circle `x^2 + y^2 -2x -6y - 10 = 0` which pass through the origin.

Explanation

Let (h, k) be the co-ordinates of the mid point. Equation of the chord whose mid point is (h, k) is
xh + yk - (x + h) - 3(y + k) - 10 = `h^2 + k^2 -2h -6k - 10`
(using `T = S_1`)
i.e., `h^2 + k^2 - k(6+y) + x + h + 3y + 3k = 0
This chord passes through the origin (0, 0)
`implies h^2 + k^2 - h - 3K = 0`
Hence, the required locus is `x^2 + y^2 -x -3y = 0`