Equation of a Circle Worksheet

Author:
Godfrey Almeida
Topic:
Circle, Equations
GeoGebra Applet

Instructions

The diagram shows a circle with centre C and radius r. The point (x, y) is a point that can lie anywhere on the circumference of the circle. Answer all the questions below in your notes. You can reveal the equation of the circle at each stage by clicking the check box, but remember to hide it before the start of each question. Alternatively, you can press the restart button on the right. Once you have answered all the questions, click the Check button at the bottom to check.

Question 1

Set the sliders as follows: a = 0 b = 0 r = 1 Can you write down the distance from the centre of the circle to the circumference and hence write down an equation for the circle?

Question 2

The point (x, y) is a point that can move anywhere on the circumference of the circle. Set the sliders as follows: a = 3 b = 0 r = 2 Can you write down the distance from the centre of the circle to the circumference and hence write down an equation for the circle?

Question 3

Can you manipulate the sliders so that you draw a circle that: Has a centre (-3, 1) Has the y axis as a tangent What is the equation of your circle?

Question 4

If the circle had a centre (-1, 1) and passed through the points (0, 3), (1, 0) and (-3, 0), what would the equation of the circle be?

Question 5

If a circle has equation (a, b) and radius r, what is the equation of the circle?

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