1. Section 11.1 Plane Curves and Parametric Equations By Kayla Montgomery and Rosanny Reyes

2. Introduction We typically think of a graph as a curve in the xy-plane generated by the set of all ordered pairs of the form (x, y) = (x, f (x)) for a ≤ x ≤ b. In regular graphs some planes on a curve can be described as functions y = sinx

3. Introduction cont. Others cannot be described as functions Plane Curve – When x and y are continuous functions of t What is t??????? Wait and See!!!! Irregular Plane Curve

4. Parameters and Parametric Equations Parameter = t Third Variable determines when an object was at a given point (x,y) Parametric Equations Writing both x and y as functions of t

5. Sketching the Curve These new points (x,y) = (f(t), g(t)) In the plane are called the graph of the curve C These points are still plotted on the (x,y) plane Each set of coordinates are determined by a value chosen for the parameter t Plotting these points in order of increasing values of t is called the curve orientation

6. Example 1 t-20123 x0-3-4-305 y-½-½ 0½13/ 2

7. Example

8. Eliminating the Parameter Parametric Equations Solve for t in one equation Substiute into second equation Rectangular equation t = 2y

9. Example

10. Adjusting the Domain After Eliminating the Parameter

11. Using a Trigonometric Identity to Eliminate a Parameter From this rectangular equation we see that the graph is an ellipse centered at (0,0), with vertices at (0,4) and (0,-4) and minor axis of length 2b = 6