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

Question

Concept Check Match each equation in Column I with its graph in Column II. I II47. A. 48. (x - 3)² + (y + 2)² = 25 B. 49. C. 50. D.

Accepted Answer

Hello, everyone. We are asked to identify the graph of the given equation we are given in parentheses, X minus seven squared plus the parentheses Y plus 13 squared equals nine. We are provided a coordinate plane where the scale of the X and Y axis appear to be one. And we predominantly see quadrant four. The first thing I notice about our equation is that it 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 I recall that R stands for our radius and HK is our center. So using the equation we are given again, we have the parentheses X minus seven squared plus the parentheses Y plus 13 squared equals nine. I'm gonna start trying to find my center matching it up. We have X minus H and we have X minus seven. So this means that H is seven for K, we have Y minus K and then we have Y plus 13. Since they have different signs, we need to write this down as a negative 13. So our center will be the 0.7 negative 13. So I'm gonna put that on my graph, I go over seven on the XX down 13 on the Y and that's the center of my circle. Next, I wanna find the radius and we're told that R squared will equal nine. So to find the radius, I take the square root of both sides and our radius will be three. It is positive because radius is a distance and distance can't be negative. So from my center, I'm gonna go up three spaces and put a dot to the right three spaces and put a dot down three spaces. Put a dot And then to the left three spaces and put a dot These are gonna be my guiding points to graph my circle. So when I graph my circle, we don't go through the center, it stays in the middle, it's the center. So I'm gonna do my best to make my circle look like a circle and hit all of my guiding points. It looks like enough like a circle. So we have a circle with a center of seven negative 13 and a radius of three. It's in quadrant four, have a nice day.

Concept Check Match each equation in Column I with its graph in Column II. I II47. A. 48. (x - 3)² + (y + 2)² = 25 B. 49. C. 50. D.

Key Concepts

Circle Equation

Graphing Techniques

Coordinate System

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