### 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**. **h** and **k** is also the **centre of the circle**.

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

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