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# Eliminate the parameter

1) x=3-2t
y=2+3t

2) x=sqrt(t)
y=1-t

3) x=4+2cos(theta)
y=1+2sin(theta)

4) x=sec(theta)
y=cos(theta)

5) x=e^2t
y=e^t

can someone help me with just one problem so i can do the rest?
thank you :)

### 3 Answers by Expert Tutors

Howard L. | Experienced Math Tutor Specializing in Test Prep & Grade Up SkillsExperienced Math Tutor Specializing in T...
5.0 5.0 (21 lesson ratings) (21)
1
1)  x=3-2t  --->  t= (3-x)/2
Replace t in the second equation   y= 2+3((3-x)/2) = 2+ 9/2-3x/2 = -3x/2 + 13/2 = -1/2(3x-13)
y=-1/2(3x-13), where x is any real number
2)  Replace t=1-y from the second equation, into the first eq.
x= sqrt(1-y), where 1-y >=0, Y<=1 and x>=0
x^2 = 1-y  --->  y= 1- x^2, where x>=0
3)  cos(theta) =(x-4)/2  --->  theta = arccos((x-4)/2), where 0 <= (x-4)/2 <= pi  --->  4<= x <=2pi+4
y= 1+2sin(arccos((x-4)/2), where 4<= x <=2pi+4
4)  theta= arcsec(x),
Y=cos(arcsec(x))  where x<=-1 or x>=1
5) x=e^(2t)  --->  ln x= ln e^(2t) = 2t ln(e) --->  t= (ln x)/2, where x>0
y=e^((ln x)/2) =e^ln (sqrt(x)) = sqrt (x), x>o
or easier way
x= e^(2t) = (e^t)^2 = y^2 , where x>0
or  y= sqrt(x), where x>0

Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.7 4.7 (175 lesson ratings) (175)
1
Daisy,
The idea is to solve one of the parametric equations for t in terms of x or y and then substitute that in the other equation giving a relationship between x and y.

1. t=(y-2)/3 and x=3-2((y-2)/3)=3-(2/3)y+4/3=(9/3)+(4/3)-(2/3)y=(13/3)-(2/3)y

so (2/3)y+x=(13/3)

The other easy one is 5. x=y2 by inspection or ln(y)=t and ln(x) =2t so ln(x)=2ln(y) or x=y2.

Jim

Elana G. | A Gator Can Chomp Away Your Accounting FearsA Gator Can Chomp Away Your Accounting F...
4.8 4.8 (39 lesson ratings) (39)
1
1) x=3-2t
y=2+3t

Set one equation equal to t.Then plug what t equals into the other equation. You are trying to get rid of the t and only be left with x and y.

X=3-2t

x-3= -2t
divide -2 by both sides

-0.5x+1.5=t

plug t into the y equation

y=2+3t

y=2+ 3(-0.5x+1.5)

y=2+ (-1.5x+4.5)

y=2-1.5x+4.5

y= -1.5x+6.5