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Find points on the curve 
at which the tangents are
(i) parallel to x-axis (ii) parallel to y-axis
Asked by Dilpreet Last Modified
Answer 
Harshit Bhardwaj
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).
read less Mayank Dadarwal
concept - for a tangent to any curve calculate dy/dx
(derivative) which is the slope of a required line at a general point(x,y).
in 1st part, tangent is parallel to x axis so the slope of the tangent is 0. so find dy/dx and equate it to zero.
in 2nd part, slope is infinite so the denominator in an expression of dy/dx should be zero (bcz 1/0 is infinite). equate it and find it.
PS: I m not posting a complete solution because if I do then you won't try by yourself.
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