10.3. Parameters and Parameter Elimination http://www.ck12.org
Practice
Eliminate the parameter in the following sets of parametric equations.
1.x= 3 t−1;y= 4 t^2 − 2 t
2.x= 3 t^2 + 6 t;y= 2 t− 1
3.x=t+2;y=t^2 + 4 t+ 4
4.x=t−5;y=t^3 + 1
5.x=t+4;y=t^2 − 5
For the parametric equationx=t,y=t^2 +1, graph over each interval oft.
6.− 2 ≤t≤− 1
7.− 1 ≤t≤ 0
8.− 1 ≤t≤ 1
9.− 2 ≤t≤ 2
10.− 5 ≤t≤ 5
- Eliminate the parameter and graph the following parametric curve:x=sint,y=− 4 +3 cost.
- Eliminate the parameter and graph the following parametric curve:x= 1 +2 cost,y= 1 +2 sint.
- Using the previous problem as a model, find a parameterization for the circle with center (2, 4) and radius 3.
- Find the parameterization for the line segment connecting the points (2, 7) and (1, 4).
- Find a parameterization for the ellipsex 42 + 25 y^2 =1. Use the fact that cos^2 t+sin^2 t=1. Check your answer with
your calculator. - Find a parameterization for the ellipse(x− 94 )^2 +(y+ 361 )^2 =1. Check your answer with your calculator.