C 4 Chapter 2 Parametric Equations Dr J

C 4 Chapter 2: Parametric Equations Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com Last modified: 30 th August 2015

Parametric vs Cartesian Equations ! A parametric equation is one where each of x, y (z etc. ) are expressed in terms of some independent parameter.

Sketching Parametric Curves Let’s just try a few values for the parameter and see what coordinates we get. . . t -3 -2 -1 0 1 2 3 x 9 4 1 0 1 4 9 y -6 -4 -2 0 2 4 6 ? 6 4 2 O -2 -4 -6 ? 2 4 6 8

Solving Problems involving Parametric Equations Q ? Q ? ?

Test Your Understanding C 4 Jan 2013 a ? b ?

Exercise 2 B 7 1 a c e ? ? ? 2 a c e ? 8 ? ? ? ? 9 5 a b ? ? ? 10 ?

Converting from Parametric Cartesian We can use substitution or well known identities to convert parametric equations into Cartesian ones. This involves eliminating the parametric variable and forming a single equation. ?

Test Your Understanding C 4 Jan 2011 ? C 4 June 2013 which double angle formula would be best here? ?

Exercise 2 C 3 c e ? ? g i 4 ? 5 ? ? C 4 Jan 2008 Q 7 ? C 4 June 2012 Q 6 Harder! ?