   Chapter 10, Problem 49RE

Chapter
Section
Textbook Problem

# Horizontal and Vertical Tangency In Exercises 49-52, find all points (if any) of horizontal and vertical tangency to the curve. L'se a graphing utility to confirm your results. x = 5 − t ,         y = 2 t 2

To determine

To calculate: All points of horizontal and vertical tangent to the curve. Confirm your results with the help of graphing utility.

Explanation

Given:

The parametric equations are x=5t, y=2t2

Calculation:

Consider the polar equation:

x=5t

y=2t2

Now, differentiating x and y with respect to t.

Then,

dxdt=ddt(5t)=ddt(5)ddt(t)=1

dydt=ddt(2t2)=2(2t)=4t

Since, dxdt cannot be zero

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