Completing the square to write equation in standard form of a circle | Algebra II | Khan Academy

TL;DR

Learn how to graph a circle by completing the square and identifying the center and radius.

Transcript

We're asked to graph the circle. And they give us this somewhat crazy looking equation. And then we could graph it right over here. And to graph a circle, you have to know where its center is, and you have to know what its radius is. So let me see if I can change that. And you have to know what its radius is. So what we need to do is put this in so... Read More

Key Insights

• 📈 Graphing a circle requires knowing its center and radius.
• 💁 Completing the square helps put the equation in a recognizable form.
• 🙃 Adding and subtracting values on both sides of the equation maintains equality.
• ❣️ The x and y terms are made into perfect squares.
• 💁 The center of the circle can be determined from the completed square form.
• 💁 The radius of the circle can also be determined from the completed square form.
• ❣️ The x term represents the x-coordinate of the center, while the y term represents the y-coordinate of the center.

Questions & Answers

Q: How do you graph a circle?

To graph a circle, you need to know the equation's center and radius. Completing the square allows you to identify these values.

Q: What does completing the square involve?

Completing the square involves making the x and y terms into perfect squares by adding and subtracting appropriate values.

Q: Why do we need to add the same values to both sides of the equation?

In order to maintain equality, any changes made to one side of the equation must also be made to the other side.

Q: How do you calculate the radius of a circle?

In the equation x-a squared + y-b squared = r squared, r represents the radius of the circle.

Summary & Key Takeaways

• To graph a circle, you need to identify its center and radius.

• Completing the square allows you to put the circle's equation into a recognizable form.

• The x and y terms are separated and made into perfect squares, allowing you to identify the center and radius.