In Exercises 53–64, complete the square and write the equation in...

Question

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+6x+2y+6 = 0

Accepted Answer

For the following circle equation completely squares. In order to write the whole equation in standard form, identify the center and radius and then graph we have X squared plus y squared plus four X plus 10. Y plus 20 equals zero. Standard form of a circle, you know, is given by x minus H squared plus y minus k squared equals r squared when they get to this form. So we're gonna complete the square by combining our like terms and trying to complete the square to find the number that fits in polynomial. Other words what I mean? The first gonna take X squared plus four X. And put them by each other. Now to complete the square we will take our terminar X before divided by two and then swear it. This number is equal to four. We will add this four at the end of this polynomial. Also the same for y. We have y squared plus 10 y. 10/2 squared is 25. So at 25. Now I'm gonna go ahead and move my 20 over as well have a positive 20 left side that turns the negative 20 on the right. Now I want to add before we added to the left And the we added to the left. Now we can do some some kitchen X squared plus four. X plus four is a polynomial that has factors We can break those factors down as X plus two squared same for the y squared polynomial. We can write that as y plus five squared and we simplify 20 negative 20 rather plus four plus 25. That gives us none. Now we can find the center, the center it's given by H. K. Look here are H. We have X plus two. Bar equation is x minus H. That's going to be a negative two. Same for the white negative facts. Our radius R squared will be equal to the right side of the equation Squared of nine. R. is equal to three. So we have all the data. We need to solve our best we can find the equation that is X plus two squared plus Y plus five squared equals nine, Centre -2 -5 and Radius III. So let's look graph A. Has the wrong equation. So it can't be graphic. A. The same for graphic. Be else has the wrong equation. See has the correct equation, the correct center and the correct radius. I think the answer is C. Let's check D just be safe. D. has an incredibly equation because it's equaling 49 and not nine. That means the answer to our problem is answer C. Okay I hope to help you solve the problem. Thank you for watching. Goodbye

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+6x+2y+6 = 0

Key Concepts

Completing the Square

Standard Form of a Circle

Graphing Circles

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