Find the points on the curve `x^2+y^2-2x-3=0`at which the tangents are parallel to the x-axis.

Explanation

Equation of curve
` x^(2)+y^(2)-2x - 3 = 0`…(1)
` rArr 2x + 2y (dy)/(dx) - 2 =0`
` rArr (dy)/(dx) = (1-x)/y`
Slope of tangent at point `(x, y) is m = (1-x)/y`
but the tangent is parallel to x-axis.
` :. M = 0`
` rArr (1-x)/y = 0 rArr x = 1`
put x = 1 in equation (1)
` 1+ y^(2) - 2 - 3 = 0`
` rArr y^(2) = 4 rArr y = pm 2`
`:.` Required point = (1, 2) and (1, -2)