At what points the slope of the tangent to the curve x2 + y2 – 2x – 3 = 0 is zero.

Q13 of 149 Page 16

At what points the slope of the tangent to the curve x² + y² – 2x – 3 = 0 is zero.

Given that the curve x² + y² – 2x – 3 = 0

Differentiation on both the sides,

According to the question,

Slope of the tangent = 0

⇒ x = 1

Putting this in equation of curve,

1 + y² – 2 – 3 = 0

⇒ y² = 4

⇒ y = ±2

So, the required points are (1, 2) and (1, -2)

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