Maths Extension 1 Year 11 - Module 1 - Lesson 9
Introduction to Parametric Equations
Name
Date
Class
1. Lesson focus
Introduction to parametric equations. Eliminate the parameter by solving one equation for t and substituting into the other; keep any restrictions on t.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. For x=t+1 and y=t², eliminate t.
3. For x=2cos t and y=3sin t, find the Cartesian equation.
3. Challenge
If x=4t+1 and y=3−2t, find y as a function of x.
4. Multiple choice
Eliminating t from x=2cos t,y=3sin t gives which curve?
A. x+y=1
B. x²+y²=1
C. y=3x/2
D. x²/4+y²/9=1
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Given x=3t−2 and y=2t+1, eliminate t.
t=(x+2)/3; y=2(x+2)/3+1=(2x+7)/3.
2. For x=t+1 and y=t², eliminate t.
t=x−1, so y=(x−1)².
3. For x=2cos t and y=3sin t, find the Cartesian equation.
(x/2)²+(y/3)²=cos²t+sin²t=1, so x²/4+y²/9=1.
Challenge. If x=4t+1 and y=3−2t, find y as a function of x.
t=(x−1)/4; y=3−(x−1)/2=(7−x)/2.
Multiple choice. Eliminating t from x=2cos t,y=3sin t gives which curve?
Correct answer: D. Divide by 2 and 3, square and add; cos²t+sin²t=1 gives the ellipse equation.
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