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Find points on the curve  at which the tangents are

(i) parallel to x-axis (ii) parallel to y-axis

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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...
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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 givesy = 0.

Then, for y = 0.

Hence, the points at which the tangents are parallel to the y-axis are

(3, 0) and (− 3, 0).

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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...
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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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Comments

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