The correct option is D (1,2) (1, -2)
Given x2+y2 -2x -3 = 0 ......(1)
Diff. w.r.t.x, we get
2x + 2ydydx - 2 = 0
⇒dydx=1−xy
Since the slope of the tangent to the curve is zero.
∴dydx = 0
⇒ 1 - x = 0
⇒ x = 1
Put x = 1 in equation (1), we get 1 + y2 -2 -3 = 0
⇒y2 = 4
⇒ y = ±2
Hence required points are (1, 2) and (1, -2)