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 + 2)² + (y - 2)² = 4

Accepted Answer

a circle is described by the equation X plus five squared plus y minus five squared equals nine graph the circle and identify center radius as well as domain and range. So I've written out the standard form of the circle being x minus x squared plus y minus k squared equals r squared. Let's go ahead and find the center. The center that's given by H comma K. We notice here the H. Is with the X. We have X plus five in our equation R. H. Then is -5. Okay Is with Ry that should be five. Now we want our radius. So radius. See my R squared. We set that equal to the right side of the equation. nine R squared equals nine. We take the square root. We get R equals three. So our radius is going to be three. Now we can use both of those to find our domain and range domain with square brackets. It will be the X. Component of our center or H. And then plus or minus our radius. So we have negative 5 -3. 1st that is negative eight negative five plus three. Now is negative two To the same for the rage. Sit down with the way five is our y. 5 -3 is two and five plus three is eight. Now, when they find a graph that has all the information we have here look at a notice we have the wrong center. So it can't be graph we want negative 55 B is the similar way we have 5 -5 in the middle. So it can't be b. See we have 95 5 but it says our radius is nine, so it can't be see either because our radius is actually wrong. Now. Finally we get D. Which has a correct center, our radius, domain and range. That means our answer is D. 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 + 2)² + (y - 2)² = 4