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. C. 50. (x + 3)² + (y + 2)² = 25 D.

Accepted Answer

Hello, everyone. We are asked to identify the graph of the given equation. The equation we are given is the parentheses X plus seven squared plus the parentheses Y plus squared equals nine. We are provided a coordinate plane where we predominantly see the third quadrant and the scale appears to be in ones. So the first thing I notice about this equation is that it reminds me of the equation of a circle. The equation of a circle is in parentheses X minus H squared plus the parentheses Y minus K squared equals R squared, which is the radius squared. So R would be our radius and our center of our circle is at HK. So now using the equation we're given, let's match this up. So again, we're given X plus seven in parentheses squared plus Y plus 13 in parentheses squared equals nine. So starting off looking for my center, I notice the formula has a negative H and we have a positive seven. So this means we have to take the opposite sign. So this will be negative seven for H. And the same thing happens for K, we were given Y minus K and we have Y plus 13. So this means a double negative happened and our K is negative 13. So I'm gonna put our center on the circle and then I'm gonna, or sorry on the coordinate plane. And then I'm gonna find the radius so I can make the full circle. So negative seven on the X and going down to negative 13 on the Y I have a point that is in the third quadrant next to find the radius, I know that R squared is gonna be nine. So R squared equals nine to find the radius, we take the square root of both sides. So our radius is three, it has to be positive because radius is a distance and distance is always positive. So from our center, I'm gonna go up three of the little dot to the right three, put a dot down three and to the left three, I put these here as a guideline for myself. So I can graph my circle. So the center will not be touched by the circle as it is the center of the circle. And I'm gonna do my best to make a circle that matches my radius. So there we are, we have a circle with a center of negative seven, negative 13 and a radius of three 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. C. 50. (x + 3)² + (y + 2)² = 25 D.

Key Concepts

Equation of a Circle

Graph Interpretation

Coordinate Geometry Basics

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