What is the equation of a circle?
In this post, we recognise features and properties of the circle graph, x^{2} + y^{2} = r^{2} and (x -a)^{2} + (x - b)^{2} = r^{2} , including their circular shapes, their centres and their radii. This is a part of the Prelim Maths Advanced course under the topic Working with Functions and sub-part Further Functions and Relations, specifically focusing on circles. We will:
- Derive the equation of a circle, centre the origin, by considering Pythagoras’ theorem and recognise that a circle is not a function
- Transform equations of the form x^{2} + y^{2} + ax +by + c =0 into the form x^{2} + y^{2} = r^{2} , by completing the square
- Sketch circles given their equations and find the equation of a circle from its graph
- Recognise that y = \sqrt{r^{2} - x^{2}} and y = -\sqrt{r^{2} - x^{2}} are functions, identify the semicircular shape of their graphs and sketch them
How do I graph a circle?
This video covers how to write your working out in graphing circle questions, showing a methodical, clearly explained step-by-step procedure when answering circle questions.
What is the equation of a semi-circle?
This video discusses the equation of a semi-circle and provides an example.
