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+3x+5y+9/4=0

Accepted Answer

The following circle equation. Complete the squares. In order to write the whole equation in standard form, identify that sitting in a radius and then graph. So standard form of a circle. It's given by x minus H squared plus y minus k squared equals r squared. We're hk it's the center R is the radius. Now we want to determine how to find standard form. We complete the square. Let's first combine our variables together. Our exes together and our wives together. I'm also gonna move my nine or 4 to the other side. You have negative four over there. I want to complete the square. So we'll work with the excess first To complete the square. We're gonna take in a polynomial. B over two squared. If you look at our X squared plus seven X. R B is going to be on the X. That would be 7/2 squared. Which is equal to 49/ suddenly fell away. R b is nine, that is nine, number two squared, It's equal to 81. Number four. I'm not going to rewrite our polynomial X squared plus seven X. Now we're gonna add on our completed square 49/4. Stand for the way we have Y squared plus nine way and we add our 81/4. Since we're adding on the left side of the equal sign will add on the right side as well. So we have negative ira four Plus 49/4 Plus 81/4. Now we're gonna factor out all of our things. So X squared seven X plus 49/4. That factors two X. Plus 7/2 squared. But why factors as Why? Plus 9/2 Squared. And on the right side this simplifies to 121/4. We also have our center our center is H. K. Which we can look here we have X plus 7/2. R. H turns into negative 7/2. Same for a while -9. Number two. Our radius R squared is 1 21/4. Take the square root R. R equals 11/2. So we have our center our radius and our equation right here Let's figure out which graph has all of these attributes. Look at graphic a. The standard form is correct and the center is correct. However our radius is not correct. That should be 11-2. So you can't say answer A. Is right answer B. The question is correct. Our center is correct and our radius is correct. So I think we have answer B. Let's check the others. Just to be safe. We'll see our equation is actually incorrect because we should have pluses and minuses and our radius is incorrect. So it can't be C. Either the same for D. It's just our equation is incorrect. That means the answer to our problem turns out to be graph B. 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+3x+5y+9/4=0

Key Concepts

Completing the Square

Standard Form of a Circle

Graphing Circles

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