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 + y² = 16

Accepted Answer

a circle is described by the equation, X squared plus y squared equals 1 21 grab the circle identifies center and radius as well as his domain and range. And as seen from the circle we know is given by x minus H squared plus y minus k squared equals r squared. We notice here we have nothing with our x squared y squared. If we have no extra numbers in there for similar form, this means our center H comma K. It's equal to 00. Now it's going to find a radius radius. We will set r squared equal to everything on the right side of the equation or 1 21. Then we'll take the square to both sides, giving us our equals 11. This makes our Radius 11. Now with the front our domain and Rich two men will be the H part of our center plus or minus R radius will use square brackets. So we have zero minus 11, which is native 11, 0 plus 11, which is positive 11. Similarly for a range, we'll use the K. This time. Zero minus 11 is negative 11. 0 plus 11 is positive 11. We have everything. We need to grab the circle. Let's take a look at their possible graphs. A has center 00 radius 11. And domain arranged from negative 11 to 11, I believe is our answer here. But let's check the others. Just to be safe. B has center 0, 11, radius 1, 21 diamonds, B is wrong. It is not matching with what we found. See says the center is 11-0 and our radius is the square root of 11, so C. Is also not correct. This is our center is 11, 11, Which means that's not correct because our sitter was 00. That means the answer to our problem. His answer, Hey, okay, 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. x² + y² = 16