Q19 of 168 Page 211

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

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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