# Equation of a Circle

## Instructions

### Play around with the sliders to change the circle

The equation for a circle, as written above, is $(x - a)^2 + (y - b)^2 = r^2$ where: $$x$$ and $$y$$ are cartesian coordinates, $$(a,b)$$ is the centre of the circle, and $$r$$ is the radius. By moving the sliders, you can change these variables, and see instantly how they reflect on what the circle looks like!

If you increase $$a$$, it will move the centre (and so the whole circle) to the right. Likewise if you decrease $$a$$ it will move to the left. Increasing or decreasing $$b$$ will move the circle up or down respectively. As $$r$$ is the radius, the circle grows or shrinks as you play with its value.

### Challenge yourself

Why not pick some values for $$a$$, $$b$$ and $$r$$, then try sketching the circle on paper? You can check your sketch by choosing matching values above.

### Zoom

You can zoom in and out using the + and - buttons in the bottom right corner. Note that there is a limit to how far you can zoom in either direction.

### Glitches?

If you find any problems or have ideas for improvements, contact by Twitter: @NextLevelMaths.