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Drag each equation to the correct location on the table. Not all equations will be used.

Place the equations that represent circles with the smallest and the largest radius into the table.

[tex]
4x^2 + 4y^2 - 16x - 24y + 51 = 0 \quad 2x^2 + 2y^2 + 16x - 4y + 30 = 0 \quad x^2 + y^2 + 6x - 4y - 20 = 0
[/tex]

\begin{tabular}{|l|l|}
\hline
Smallest Radius Length & Largest Radius Length \\
\hline
& \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To determine the radii of the given circle equations, let's analyze each equation step-by-step.

### 1. Analyzing the Equation [tex]\(4x^2 + 4y^2 - 16x - 24y + 51 = 0\)[/tex]
From our calculations,
- The radius for this equation is determined to be 0.5.

### 2. Analyzing the Equation [tex]\(2x^2 + 2y^2 + 16x - 4y + 30 = 0\)[/tex]
From our calculations,
- The radius for this equation is determined to be 1.41421356237310 (which is approximately [tex]\(\sqrt{2}\)[/tex]).

### 3. Analyzing the Equation [tex]\(x^2 + y^2 + 6x - 4y - 20 = 0\)[/tex]
From our calculations,
- The radius for this equation is determined to be 5.74456264653803.

Given these radii, let's assign the equations to the appropriate categories:

#### Smallest Radius Length
- Equation: [tex]\(4x^2 + 4y^2 - 16x - 24y + 51 = 0\)[/tex]
- Radius: 0.5

#### Largest Radius Length
- Equation: [tex]\(x^2 + y^2 + 6x - 4y - 20 = 0\)[/tex]
- Radius: 5.74456264653803

Now we can complete the table:

[tex]\[ \begin{tabular}{|l|l|} \hline Smallest Radius Length & Largest Radius Length \\ \hline 4x^2 + 4y^2 - 16x - 24y + 51 = 0 & x^2 + y^2 + 6x - 4y - 20 = 0 \\ \hline \end{tabular} \][/tex]

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