Question

Find points on the curve x²/9+y²/16=1 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  -16x/9y is 0 which is possible

 if 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

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