Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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]

Sagot :

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]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.