Question

Find points on the curve at which the tangents are

(i) parallel to x-axis (ii) parallel to y-axis

Answer 1

The equation of the given curve is.

On differentiating both sides with respect to x, we have:

(i) The tangent is parallel to the x-axis if the slope of the tangent is i.e., 0 which is possible if x = 0.

Then, for x = 0

Hence, the points at which the tangents are parallel to the x-axis are

(0, 4) and (0, − 4).

(ii) The tangent is parallel to the y-axis if the slope of the normal is 0, which gives⇒ y = 0.

Then, for y = 0.

Hence, the points at which the tangents are parallel to the y-axis are

(3, 0) and (− 3, 0).