By Team Aakash Byju's | 27th January 2023
Parallel to the x-axis.
The points at which the tangents are parallel to the x-axis are (0,4) and (0,−4).
The points at which the tangents are parallel to the y-axis are (3,0) and (−3,0).
A
B
C
Given,
differentiating this with respect to x on both sides, we get
(3,0)
(-3,0)
(0,4)
(0,-4)
Now, for a tangent to be parallel to the x-axis, its slope has to be zero because it will be a horizontal line.
(3,0)
(-3,0)
(0,4)
(0,-4)
But this is possible only if x=0
Then
for x=0, => y =16 => y= 4
Therefore the points are (0, 4) and (0, −4)
(3,0)
(-3,0)
(0,4)
(0,-4)
Now, for a tangent to be parallel to the y-axis, the slope of its normal has to be zero.
(3,0)
(-3,0)
(0,4)
(0,-4)
Then ,
Therefore the points are (3, 0) and (−3, 0)
for y=0, => x= 3
(3,0)
(-3,0)
(0,4)
(0,-4)