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 + 1)² + y² = 25

Accepted Answer

a circle is described by the equation X plus five squared plus y squared equals 16. Grab the circle identify center radius as well as his domain and Rage. So it's going to take a look. Let's find our center first. The center is given by H comma K. In a standard form of a cycle. The equation is x minus H squared plus y minus k squared equals r squared. So I feel like in our equation we can see that we have X plus five squared Our center, then we'll be at negative five or page zero for Y because there's nothing in our Y. So I center is at negative 50. The radius will be R squared equal to whatever number we have on the right side of the equal side. 16. Then we solve for R squared to both sides. R is equal to four. So we have a radius of four. Now I want our domain or rich. Our domain will be the center of the circle plus Arabia's and our center of a circle minus the radius. So he would care center circle is at negative five. If I would subtract four I would get negative none. Or to add for our get -1. Same for the range Except now on the way I'm starting at H equals zero. I subtract four. I get negative four by ad for I just get positive for so our center radius domain and range are shown here. Let's look at our answers and see if we have a circle that matches all this data answer. A as an incorrect center is on the wrong side of the graph so it can't be answered A. It also has an incorrect radius B. So has an incorrect center, but it has the correct radius. However we're on the wrong side, so it can't be be either. C. Has a correct center. However the radius incorrect, the radius should be four, so it can't be C. Either. Look at D. We notice our center is 9 to 50 races four and our domain and range match. That means the answer to our equation and our question is the answer. D. Okay, 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. (x + 1)² + y² = 25

Key Concepts

Circle Equation

Graphing Circles

Domain and Range

Watch next