KKhaemenes PrecalculusTeacher Answer Key
Student Lesson

Teacher Key · Unit 09 · Lesson 05

Parametric Equations and Eliminating the Parameter

Use this key to verify method, notation, domain, units, and interpretation. Accept equivalent exact forms when mathematically valid.

Khaemenes Academy · Teacher Key

Parametric Equations and Eliminating the Parameter

U09 · L05
1

Eliminate t from x=2t+1, y=3t−4.

Parametric visualDescribe motion and curves with a shared parameter, eliminate parameters when possible, and interpret direction, velocity, and time. xyvₓvᵧ
Answer: y=(3/2)x−11/2
Reasoning: Solve t=(x−1)/2 and substitute.
2

For x=cos t, y=sin t, identify the curve.

Parametric visualDescribe motion and curves with a shared parameter, eliminate parameters when possible, and interpret direction, velocity, and time. xyvₓvᵧ
Answer: Unit circle
Reasoning: x²+y²=1.
3

At t=2, find the point for x=t², y=3t.

Parametric visualDescribe motion and curves with a shared parameter, eliminate parameters when possible, and interpret direction, velocity, and time. xyvₓvᵧ
Answer: (4,6)
Reasoning: Substitute t=2.
4

What information is lost when eliminating a parameter?

Parametric visualDescribe motion and curves with a shared parameter, eliminate parameters when possible, and interpret direction, velocity, and time. xyvₓvᵧ
Answer: Direction and timing
Reasoning: The Cartesian equation retains only the locus.
5

A projectile has x=20t, y=30t−5t². Find x at t=3.

Parametric visualDescribe motion and curves with a shared parameter, eliminate parameters when possible, and interpret direction, velocity, and time. xyvₓvᵧ
Answer: 60
Reasoning: x=20(3).
6

For x=4cos t, y=2sin t, identify the curve.

Parametric visualDescribe motion and curves with a shared parameter, eliminate parameters when possible, and interpret direction, velocity, and time. xyvₓvᵧ
Answer: Ellipse x²/16+y²/4=1
Reasoning: Square and add normalized equations.
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