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

Question

Philoid · Accepted Answer

Since the tangent is parallel to y–axis, its slope is not defined, then the normal is parallel to x–axis whose The Slope is zero.

i.e., = 0

⇒ = 0

⇒ y = 0

Substituting y = 0 in = 1,

= 1

⇒ x² = 9

⇒ x = ±3

Thus, the required point is (3,0) & ( – 3,0)