question_answer 45)

Find the points on the curve  at which the tangents are (a) parallel to X-axis (b) parallel to Y-axis.  

Answer:

Let P(h, k) be the required point on                                            ?. (1)                                            ?. (2)       Diff. (1) w.r.t. x                    m = slope of tangent to (1)             (a) The tangent to (1) are ||X-axis         m = 0         h = 0             k = ± 4       (b) k = ± 4        Required points are (0, ±4). (II)   The tangents to (1) are || Y-axis              is not defined.                   (b)h = ± 3        Required points are (± , 0).