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

General Form:
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]
5. [tex]\(2x^2 + 2y^2 - 24x - 16y - 8 = 0\)[/tex]
6. [tex]\(x^2 + y^2 + 2x - 12y - 9 = 0\)[/tex]

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

Pair the 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] ->
5. [tex]\(2x^2 + 2y^2 - 24x - 16y - 8 = 0\)[/tex] ->
6. [tex]\(x^2 + y^2 + 2x - 12y - 9 = 0\)[/tex] ->

Sagot :

GinnyAnswer
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]
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