Answer :

(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).


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