This worksheet is aimed at deepening understanding of the equation of a circle.
Starting discussion points could include:
- What are the possible arrangements of two circles (e.g. concentric, one point in common, no points in common, etc)? Students could then be asked to give values for the coordinates of the centre and the radii for each arrangement and these could be tested.
- Explain why all the points on the circle satisfy the given equation.
Some possible question prompts for students are:
- Change one slider so that the circles intersect at two distinct points.
- Change the sliders so that both circles sit in the first quadrant and each touch the x- and y-axes but not each other.
- Hide the red circle and set c=d=1 and Radius=2. Adjust one slider so that the circle appears in 3 quadrants. What range of values give solutions?
