E3 (adv) - write the equations of circles and ellipses in transformational form and as mapping rules to visualize and sketch graphs.

Lindsay

Definitions:

Circle: a single, closed curved line

Ellipse: a single, closed curved line that has one axis longer than the other (x-axis or y-axis) *Example below has a longer y-axis*

Writing an equation for a circle: To write an equation for a circle, it first needs to be put on a graph. Let's make it easy and have the centre of the circle at the origin of the graph (0,0).

The equation of a circle looks like this: [1/r (x-h)]^2 + [1/r (y-k)]^2 = 1  This is called Transformational Form. The r stands for radius, h is the horizontal translation and k is the vertical translation.

The equation for the circle above is: [1/5 (x-0)]^2 + [1/5 (y-0)]^2 = 1

If we only had the equation and not the diagram of the circle, we would need a mapping rule. A mapping rule looks like this: (x,y) -> (x