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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Match the circle equations in general form with their corresponding equations in standard form.

[tex]\[
\begin{array}{ll}
x^2 + y^2 - 4x + 12y - 20 = 0 & (x-6)^2 + (y-4)^2 = 56 \\
x^2 + y^2 + 6x - 8y - 10 = 0 & (x-2)^2 + (y+6)^2 = 60 \\
3x^2 + 3y^2 + 12x + 18y - 15 = 0 & (x+2)^2 + (y+3)^2 = 18 \\
5x^2 + 5y^2 - 10x + 20y - 30 = 0 & (x+1)^2 + (y-6)^2 = 46 \\
2x^2 + 2y^2 - 24x - 16y - 8 = 0 & x^2 + y^2 + 2x - 12y - 9 = 0
\end{array}
\][/tex]



Answer :

GinnyAnswer
Sure, let's match each circle equation in its general form to its corresponding equation in the standard form. We'll need to pair the equations correctly.

General Form Equations:
1. [tex]\( x^2 + y^2 - 4x + 12y - 20 = 0 \)[/tex]
2. [tex]\( x^2 + y^2 + 6x - 8y - 10 = 0 \)[/tex]
3. [tex]\( 3x^2 + 3y^2 + 12x + 18y - 15 = 0 \)[/tex]
4. [tex]\( 5x^2 + 5y^2 - 10x + 20y - 30 = 0 \)[/tex]

Standard Form Equations:
1. [tex]\( (x - 6)^2 + (y - 4)^2 = 56 \)[/tex]
2. [tex]\( (x - 2)^2 + (y + 6)^2 = 60 \)[/tex]
3. [tex]\( (x + 2)^2 + (y + 3)^2 = 18 \)[/tex]
4. [tex]\( (x + 1)^2 + (y - 6)^2 = 46 \)[/tex]

Here's the correct matching:

1. [tex]\( x^2 + y^2 - 4x + 12y - 20 = 0 \)[/tex]
- Corresponds to: [tex]\( (x - 6)^2 + (y - 4)^2 = 56 \)[/tex]

2. [tex]\( x^2 + y^2 + 6x - 8y - 10 = 0 \)[/tex]
- Corresponds to: [tex]\( (x - 2)^2 + (y + 6)^2 = 60 \)[/tex]

3. [tex]\( 3x^2 + 3y^2 + 12x + 18y - 15 = 0 \)[/tex]
- Corresponds to: [tex]\( (x + 2)^2 + (y + 3)^2 = 18 \)[/tex]

4. [tex]\( 5x^2 + 5y^2 - 10x + 20y - 30 = 0 \)[/tex]
- Corresponds to: [tex]\( (x + 1)^2 + (y - 6)^2 = 46 \)[/tex]

Our final pairs are:
1. [tex]\( x^2 + y^2 - 4x + 12y - 20 = 0 \)[/tex] → [tex]\( (x - 6)^2 + (y - 4)^2 = 56 \)[/tex]
2. [tex]\( x^2 + y^2 + 6x - 8y - 10 = 0 \)[/tex] → [tex]\( (x - 2)^2 + (y + 6)^2 = 60 \)[/tex]
3. [tex]\( 3x^2 + 3y^2 + 12x + 18y - 15 = 0 \)[/tex] → [tex]\( (x + 2)^2 + (y + 3)^2 = 18 \)[/tex]
4. [tex]\( 5x^2 + 5y^2 - 10x + 20y - 30 = 0 \)[/tex] → [tex]\( (x + 1)^2 + (y - 6)^2 = 46 \)[/tex]

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