Concept Check Match each equation in Column I with its graph i...

Question

Concept Check Match each equation in Column I with its graph in Column II. I II 47. A. 48. B. 49. (x + 3)² + (y - 2)² = 25 C. 50. D.

Accepted Answer

Hello, everyone. We are asked to identify the graph of the given equation. The equation we are given is in parentheses X plus seven squared plus the parentheses Y minus squared equals nine. We were provided a coordinate plane where the X and Y axis appear to have a scale of one. And we predominantly see quadrant two looking at the equation we're given, I recall that this looks very similar to the equation of a circle which is in parentheses, X minus H squared plus the parentheses Y minus K squared equals R squared. And in this form, I remember that my center is the point HK and the R represents our radius. So now let's match that up to the equation we're given. So X plus seven in parentheses squared plus Y minus 13 in parentheses squared equals nine. So first, I'm gonna find my center. So H we had X minus H and we are given X plus seven. This means at some point we had a double negative. So we are gonna say this is negative seven as the H for the K, we have Y minus K and we have Y minus 13 since they're both minuses. We're gonna take this as a positive 13. So our center will be at the point negative 7 13. So I'm gonna place that on the graph negative seven on the X 13 on the Y. And now I want to find the radius. So we are told R squared equals nine. So to find the radius, we take the square root of both sides. So RR radius will equal three and it's a positive three because radius is a distance and distance cannot be negative. So from our center, I'm gonna go up three places and put a guiding dot to the right three places and put a guiding point down three places. Put a guiding point into the left three places and putting a guiding point. These points are to help me make my circle, our circle will not go through the center. It is the center. So it'll stay in the middle. So now I'm gonna try my best to make something that looks like a circle connecting those dots. And there we go, we have a circle with a center of negative 7 and a radius of three. It's in the second quadrant. Have a nice day.

Concept Check Match each equation in Column I with its graph in Column II. I II 47. A. 48. B. 49. (x + 3)² + (y - 2)² = 25 C. 50. D.

Key Concepts

Equation of a Circle

Graph Matching Techniques

Coordinate Geometry and Transformations

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