Q. 194.1( 22 Votes )
Find the points on the curve x2 + y2 – 2x – 3 = 0 at which the tangents are parallel to the x-axis.
Answer :
It is given that x2 + y2 – 2x – 3 = 0
Now, differentiating both sides with respect to x, we get
We know that the tangents are parallel to the x –axis if the slope of the tangent is 0 ie,
⇒ 1-x = 0
⇒ x = 1
But, x2 + y2 – 2x – 3 = 0 for x = 1
⇒ y2 = 4
⇒ y = 
2
Therefore, the points at which the tangents are parallel to the x-axis are (1,2) and (1, -2).
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