Write the equation of the circle centered at with diameter 12 .
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To write the equation of a circle, we can use the standard form, which is , where is the center of the circle and is the radius. Given that the center is at and the diameter is 12, the radius will be 6. Plugging these values in, we get:

So, that’s your equation!

Now, it’s easier than you think to visualize circles! If you imagine drawing your circle by starting at the center and then moving outwards in all directions to form a perfect round shape, you can easily explore its properties, such as where it intersects the axes or its distance from other shapes. It’s like finding where your pizza overlaps with the table!

When working with the equation of a circle, a common mistake is to forget to square the radius when writing the equation. This happens because it can be easy to confuse the radius with its diameter. Always double-check your calculations! Another tip is to plot points on the graph: it helps reinforce how the circle expands from the center—think of it as connecting the dots to create the perfect pizza!