   Chapter 10.3, Problem 29E

Chapter
Section
Textbook Problem

Finding Equations of Tangent Lines InExercises 27-30, find the equations of the tangent lines at the point where the curse crosses itself. x = t 2 − t , y = t 3 − 3 t − 1

To determine

To Calculate: The equation of tangent at point where curve crosses itself.

Explanation

Given: x=t2t&y=t33t1

Explanation:

Calculation:

x=t2t&y=t33t1

Differentiate both functions with respect to t

dxdt=2t1

dydt=3t23

Graph of parametric equation is given below:

From the above figure curve crosses itself when (x,y)=(2,1)

Substitute (x,y)=(2,1) in the parametric equation,

t2t=2

t2t2=0

t22t+t2=0

t(t2)+1(t2)=0

(t2)(t+1)=0

t=1,2

t23t1=1

t23t2=0

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