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Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis.
Asked by Nayana Last Modified
Answer 
Harshit Bhardwaj
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 ⇒
Hence, the points at which the tangents are parallel to the x-axis are (1, 2) and (1, −2).
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