   Chapter 10.3, Problem 29E

Chapter
Section
Textbook Problem

# Horizontal and Vertical Tangency In Exercises 29–38, find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. x = 4 − t ,         y = t 2

To determine

To calculate: The points of horizontal and vertical tangent to curve x=4t,y=t2 and confirm by the use of a graphical utility.

Explanation

Given:

The function x=4t,y=t2.

Formula used:

The condition for horizontal tangent is dydt=0 and the condition for vertical tangent is dxdt=0.

Calculation:

As given in the function:

x=4t,y=t2

Differentiate these both with respect to t,

dxdt=1

And,

dydt=2t

The condition for horizontal tangent is dydt=0.

Put the value of dydt,

2t=0t=0

Put the value of t in the function,

x=4t=40=4

And,

y=t2=(0)2=0

Hence, the point for horizontal tangent is (4,0).

Similarly, the condition for vertical tangent is dxdt=0

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