Year 2 Chapter 8: Parametric Equations

Question 1

What is a parameter and how is it often represented?

Answer 1

. You can write x and y coordinates of each point on a curve as functions of a third variable.
. This variable is called a parameter and it often presented by the letter ‘t’.
. A curve can be defined using parametric equations ‘x=p(t)’ and ‘y=q(t)’.
- Each value of the parameter, t, defines a point on the curve with coordinates (p(t),q(t)).

Question 2

What is a Cartesian equation (in two dimensions)?

Answer 2

An equation that only involves the variables x and y.

Question 3

For parametric equations ‘x=p(t)’ and ‘y=q(t)’ with Cartesian equation ‘y=f(x)’, what is the domain and range of f(x) equivalent to?

Answer 3

. Domain of f(x) = range of p(t).

. Range of f(x) = range of q(t).

Question 4

For parametric equations ‘x=p(t)’ and ‘y=q(t)’ with Cartesian equation ‘y=f(x)’, how do you find what y=f(x) is when you are given the 2 parametric equations?

Answer 4

. For x=p(t), rearrange to get ‘t’ on it’s own.
. Replace what ‘t’ is equivalent to the ‘t(s)’ in ‘y=q(t)’ so you get a Cartesian equation, consisting of x and y values.
. Simplify Cartesian equation to get y=f(x).