Identifying Properties of a Circle
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Practice Quiz 22 Identify the center and radius of each. Then sketch the 1) $(x + 2)^2 + (y - 4)^2 = 5$
This question includes visual content: A Cartesian coordinate system graph with both x and y axes ranging from -8 to 8. The grid consists of unit squares. Below the axes is blank space for sketching. The question text asks to identify the center and radius of the equation (x+2)^2 + (y-4)^2 = 5 and to use the graph to sketch it.
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In this problem, we need to identify the center and radius of a circle from its equation, and then sketch it on a grid.
Circle Equation Analysis
Let's start by writing down the standard form of a circle's equation. It is x minus h squared plus y minus k squared equals r squared.
Now, let's look at the given equation: x plus two squared plus y minus four squared equals five.
To find the center, h comma k, we compare the components. Since the standard form has a minus sign, x plus two is the same as x minus negative two.
This means h is negative two and k is positive four. So, the center of our circle is at the point negative two, four.
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