Find the point on the curve at which the tangents are parallel to x – axis

Given:

The curve is = 1

Differentiating the above w.r.t x, we get the Slope of tangent,

⇒ = 0

⇒ = 0

Cross multiplying we get,

⇒ = 0

⇒ 16x + 9y = 0

⇒ 9y = – 16x

⇒ = ...(1)

(i)

Since, the tangent is parallel to x – axis

⇒ = tan(0) = 0 ...(2)

tan(0) = 0

= The Slope of the tangent = tan

From (1) & (2),we get,

⇒ = 0

⇒ – 16x = 0

⇒ x = 0

Substituting x = 0 in = 1,

= 1

⇒ y² = 16

⇒ y = ±4

Thus, the required point is (0,4) & (0, – 4)