Equations of Circles centred at Origin
Maths: Edexcel A Level Pure Maths, topic 3.2.1
Circles
We can look at the properties of circles by treating them as graphs in the Cartesian plane.
Definition
- A circle is defined as the set of points in a plane that are of equal distance to a fixed point called the center.
- This equal distance is called the radius.
Step 1
- A straight line touches the circumference (point P), and the origin (0,0).
- This is the hypotenuse of the right angled triangle. The other sides are 'x' and 'y'.
Step 2
- This is the equation of a circle.
Test yourself on Equations of Circles centred at Origin
A straight line touches the circumference at (3,5). What is the equation of the circle?
A straight line touches the circumference (9,4), and the origin (0,0). This is the hypotenuse of a right angled triangle. What is the length of the hypotenuse?
A straight line touches the circumference (5,12), and the origin (0,0). This is the hypotenuse of the right angled triangle. What is the length of the hypotenuse?