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

Answers (1)

parellel to x-axis means slope is 0
Given equation of curve is
x^2 + y^2 - 2x - 3 = 0
Slope of  tangent =
 -2y\frac{dy}{dx} = 2x -2\\ \frac{dy}{dx} = \frac{1-x}{y} = 0\\ x= 1
When x = 1 ,

 -y^2 = x^2 -2x-3= (1)^2-2(1)-3 = 1-5=-4
                      y = \pm 2
Hence, the coordinates are (1,2) and (1,-2)

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