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 - 2x + y² – 15 = 0

Accepted Answer

the following circle equation complete the squares. In order to write the whole equation in Standard form, identify the center and radius and then graph. So let's go ahead and look at this one, I'm going to rewrite my problem just a little bit. Just get it in standard form. So standard form is x squared plus y squared equals r squared. So let's go ahead and rewrite this. I've been with my 27 over first. If x squared minus six X plus y squared equals 27. Now we're gonna complete the square with the X squared minus six X. Because that is our only term. We need to find in this case. Now completing the square. What we're gonna do is we're gonna take our middle number B of our quadratic, Take B over two and then square it. So we will have 6/2 squared which is nine. Now we're gonna take that nine added to both sides. You will get x squared minus six X plus or nine plus y squared equals 27 plus nine or x squared minus six. X plus nine plus Y squared equals 36. Now we can factor out our x squared minus six X plus nine. Because we want a form, X squared take this this factors out two x minus three squared Plus one Squared equals 36. Now this will work for standard form because standard form is also written as x minus H squared plus y minus k squared equals r squared where our center is at the point h comma K. So if you look here, our center R. H. is our number with the X. That's gonna be three R. K. Since there's no number with the Y squared. But asleep as zero. So our center happens at 30. And finally the radius. If we know r squared is equal to 36. Our radius will then be the square of 36 or six. So we have our equation x minus three squared plus y squared equals 36. Radius equals six. And the center is three comma zero. Let's see which one of our answers. Has all this information. A has the correct equation and center but it doesn't have the right radius. It says race is 12 so the answer is not going to be a. B has a correct equation, correct center and correct radius. So I believe our answer is B. Let's check the others just to be sure. See actually as a center of negative three Which is not correct because our sinner is positive three and finally D. Is in the same boat. That's incorrect sir. And incorrect radius. That means the answer to our problem. This answer be and we can see the graph right here on the right. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye

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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 - 2x + y² – 15 = 0