(Q9) Sample #1, Math 141/146 common final, Glendale community college

TL;DR

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

Transcript

okay for number nine we are going to graph the equation x squared plus y squared minus 2y is equal to 8. the difference between this equation and the equation i did earlier is that here we have both the x and y being squared we have the x squared and the y squared together this is going to turn out to be an equation for the circle and the formula t... Read More

Key Insights

• 🟨 The equation x squared plus y squared minus 2y is equal to 8 can be graphed as a circle.
• 💁 Completing the square helps to rewrite the equation in the form of a circle.
• 😘 The center of the circle is determined by the values of h and k in the equation.
• 🍉 The radius can be identified by the term being squared in the equation.
• 🙃 Adding a number on both sides of the equation is crucial for completing the square.
• 🕡 The formula for a circle equation is x minus h squared plus y minus k squared equals r squared.
• 🧑‍🏭 The y terms in the equation must have the same factors after completing the square.

Questions & Answers

Q: How can the equation x squared plus y squared minus 2y is equal to 8 be graphed as a circle?

To graph the equation as a circle, we need to complete the square for the y terms and rewrite it in the form x minus h squared plus y minus k squared equals r squared.

Q: How do you complete the square for the equation?

To complete the square, divide the coefficient of the y term by 2, square the result, and add that number on both sides of the equation.

Q: What is the significance of adding a number on both sides of the equation?

Adding a number on both sides allows us to rewrite the equation in the form of a circle by factoring the y terms and identifying the center and radius.

Q: How can the center and radius of the circle be determined from the equation?

The center of the circle is represented by (h, k), where h is the x-coordinate and k is the y-coordinate. The radius is determined by the term being squared, in this case, 3.

Summary & Key Takeaways

• The equation x squared plus y squared minus 2y is equal to 8 can be graphed as a circle using the formula x minus h squared plus y minus k squared is equal to r squared.

• To complete the square, divide the number in front of the y by 2, square it, and then add that number on both sides of the equation.

• The completed square equation can be rewritten in the form of a circle equation with the center at (h, k) and a radius of r.