Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Let's pair the given circle equations in general form with their corresponding equations in standard form step-by-step.
1. Equation in General Form: [tex]\(x^2 + y^2 - 4x + 12y - 20 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x - 2)^2 + (y + 6)^2 = 60 \)[/tex]
2. Equation in General Form: [tex]\(x^2 + y^2 + 6x - 8y - 10 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x + 3)^2 + (y - 4)^2 = 25 \)[/tex]
3. Equation in General Form: [tex]\(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x + 2)^2 + (y + 3)^2 = 18 \)[/tex]
4. Equation in General Form: [tex]\(5x^2 + 5y^2 - 10x + 20y - 30 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x + 1)^2 + (y - 6)^2 = 46 \)[/tex]
5. Equation in General Form: [tex]\(2x^2 + 2y^2 - 24x - 16y - 8 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x - 6)^2 + (y - 4)^2 = 56 \)[/tex]
So, the correct pairs are:
- [tex]\( x^2 + y^2 - 4x + 12y - 20 = 0 \)[/tex] and [tex]\( (x - 2)^2 + (y + 6)^2 = 60 \)[/tex]
- [tex]\( x^2 + y^2 + 6x - 8y - 10 = 0 \)[/tex] and [tex]\( (x + 3)^2 + (y - 4)^2 = 25 \)[/tex]
- [tex]\( 3x^2 + 3y^2 + 12x + 18y - 15 = 0 \)[/tex] and [tex]\( (x + 2)^2 + (y + 3)^2 = 18 \)[/tex]
- [tex]\( 5x^2 + 5y^2 - 10x + 20y - 30 = 0 \)[/tex] and [tex]\( (x + 1)^2 + (y - 6)^2 = 46 \)[/tex]
- [tex]\( 2x^2 + 2y^2 - 24x - 16y - 8 = 0 \)[/tex] and [tex]\( (x - 6)^2 + (y - 4)^2 = 56 \)[/tex]
1. Equation in General Form: [tex]\(x^2 + y^2 - 4x + 12y - 20 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x - 2)^2 + (y + 6)^2 = 60 \)[/tex]
2. Equation in General Form: [tex]\(x^2 + y^2 + 6x - 8y - 10 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x + 3)^2 + (y - 4)^2 = 25 \)[/tex]
3. Equation in General Form: [tex]\(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x + 2)^2 + (y + 3)^2 = 18 \)[/tex]
4. Equation in General Form: [tex]\(5x^2 + 5y^2 - 10x + 20y - 30 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x + 1)^2 + (y - 6)^2 = 46 \)[/tex]
5. Equation in General Form: [tex]\(2x^2 + 2y^2 - 24x - 16y - 8 = 0\)[/tex]
- Corresponding Equation in Standard Form: [tex]\( (x - 6)^2 + (y - 4)^2 = 56 \)[/tex]
So, the correct pairs are:
- [tex]\( x^2 + y^2 - 4x + 12y - 20 = 0 \)[/tex] and [tex]\( (x - 2)^2 + (y + 6)^2 = 60 \)[/tex]
- [tex]\( x^2 + y^2 + 6x - 8y - 10 = 0 \)[/tex] and [tex]\( (x + 3)^2 + (y - 4)^2 = 25 \)[/tex]
- [tex]\( 3x^2 + 3y^2 + 12x + 18y - 15 = 0 \)[/tex] and [tex]\( (x + 2)^2 + (y + 3)^2 = 18 \)[/tex]
- [tex]\( 5x^2 + 5y^2 - 10x + 20y - 30 = 0 \)[/tex] and [tex]\( (x + 1)^2 + (y - 6)^2 = 46 \)[/tex]
- [tex]\( 2x^2 + 2y^2 - 24x - 16y - 8 = 0 \)[/tex] and [tex]\( (x - 6)^2 + (y - 4)^2 = 56 \)[/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.