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. (x+3)² + (y + 2)² = 4

Accepted Answer

a circle is described by the equation X plus eight squared plus y plus nine squared equals 81 graph. The circle identified center radius as well as its domain and range. So we know this informal circle is given by x minus H squared plus y minus k squared equals r squared. The center is at H comma K. Now I feel like in the graph and also you have an eight with the H&M. nine with the K. So H is -8. Ry as negative none. Which makes up the center of our circle. Now the radius is given by R squared equaling the number on the right side of the equal sign 81. In this case we take the square into both sides. We get R equals nine. So our radius is nine. Now you're gonna find the domain. The domain will be at the square bracket and we will take our H and add or subtract our radius nut. Sea of -8 -9 which gives us - 98 plus nine which gives us what? Same with the radius? I'm sorry not a radius. R. Range arrange will be the K plus or minus our radius. So we have negative nine minus nine which gives us negative 18 negative nine plus nine which gives us zero. We now have all the data. We need to make the graph. Let's go and check our possible graphs, graph A has a correct center has a radius and it has the correct domain range. I believe my answer is A. But let's check the others just to be safe notice B. It has a crack center and radius. However, we don't have square brackets on our domain, and range B is gonna be wrong because you don't have to correct brackets. See we have the incorrect center, so it can't be C. Either. And the same situation for D. That means the answer to our problem turns out to be answer. A. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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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. (x+3)² + (y + 2)² = 4