Question

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

Answer 1

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

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