Question

Find the points on the curve x² + y² − 2x − 3 = 0 at which the tangents are parallel to the x-axis.

Answer 1

The equation of the given curve is x² + y² − 2x − 3 = 0.
On differentiating with respect to x, we have:

Now, the tangents are parallel to the x-axis if the slope of the tangent is 0.

But, x² + y² − 2x − 3 = 0 for x = 1.
y²=4 ⟹ =±2

Hence, the points at which the tangents are parallel to the x-axis are (1, 2) and (1, −2).