In Exercises 41–52, give the center and radius of the circle desc...

Question

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. x² + (y − 1)² = 1

Accepted Answer

a circle is described by the equation X squared plus y minus three squared equals 16. So when they grab the circle, identify center radius and its domain and range. So the center forum for circle is given by the equation x minus H squared plus y minus k squared equals r squared. Where center happens at H K. We can notice here our equation we don't have an H. Because there's nothing in our X. That means the center will be at zero for the X. Now the Y has a -3 attached to it. That means RK is going to be three. So our center happens at 0:03. Now the radius depends on the right side of the equal side. Our square will be set equal to 16. The salt are we take the square root? So R is equal to four. That means our radius is four. Now I will check. Are done mate are the main will be our center. Sorry. H in this case plus our radius or minus our radius. Let's say we take our age minus radius first. We have zero minus four. That is negative four. Zero plus four is positive for that means our domain is from negative 4 to 4. Same for the range he said. Now we'll use the way our center is 03. We subtract four from three. We get negative one and we add four the three we get seven. So our range is from negative 1 to 7. Let's see if we have a graph that corresponds with all this data we just found graph A says we have center 03 radius four domain negative 4 to 4 and range negative 1 to 7. That's exactly what we got. Let's check the others. Just to be sure, B says center 03, radius four domain negative 44 and negative 17. You noticed there that these are actually the same sets of data except for one thing in a. The domain as rounded parentheses on it. Where B has brackets on it. You notice I use brackets earlier. This is because We are able to reach all parts of our domain so we're able to reach negative four and we're also able to reach four by the brackets imply that we can't reach those numbers. But since we can we're actually going to say is wrong here and that B is probably a correct answer. Like you see we notice our centers is off from what we would have so it can't be seen either and D is in a similar way. That means the answer to our problem is actually answered. B Okay. I hope to help you solve the problem. Thank you for watching. Goodbye

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. x² + (y − 1)² = 1

Key Concepts

Equation of a Circle

Graphing Circles

Domain and Range of a Circle

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