(i) It is given that

Now, differentiating both sides with respect to x, we get

We know that the tangent is parallel to the x –axis if the slope is 0 ie,

, which is possible if x =0

Then, for x =0

⇒ y² = 16

⇒

Therefore, the points at which the tangents are parallel to the x-axis are (0,4) and (0, -4).

(ii) It is given that

Now, differentiating both sides with respect to x, we get

We know that the tangent is parallel to the y–axis if the slope of the normal is 0 ie,

,

⇒ y = 0

Then, for y =0

⇒

Therefore, the points at which the tangents are parallel to the y-axis are (3,0) and (-3,0).