The document contains solutions to several circle equations: - The circles (x-2)^2 + (y+1)^2 = 16 and (x-h)^2 + (y-k)^2 = r^2 have center (2, -1) and radius 4. - The circle x^2 + y^2 + 6x + 2y + 6 = 0 has center (-3, -1) and radius 2. - The circle x^2 + 4x + 4 + y^2 - 10y + 25 = 9 has center (-2, 5) and radius 3.

3. 𝑥 − 2 2
+ (𝑦 + 1)2
= 16
𝑥 − ℎ 2
+ 𝑦 − 𝑘 2
= 𝑟2
𝑥 − ℎ 2
+ 𝑦 − 𝑘 2
= 𝑟2
𝑥 − 2 2
+ (𝑦 + 1)2
= 42
ℎ = 2 𝑘 = −1
• 𝐶 = (2, −1)
• 𝑟 = 4

4. 𝑥2
+ 𝑦2
+ 6𝑥 + 2𝑦 + 6 = 0
• 𝑥2
+ 𝑦2
+ 6𝑥 + 2𝑦 + 6 = 0
• 𝑥2
+ 6𝑥 + 𝑦2
+ 2𝑦 = −6
• 𝑥 + 3 2
− 9 + 𝑦 + 1 2
− 1 = −6
• 𝑥 + 3 2
+ 𝑦 + 1 2
= −6 + 9 + 1
• 𝑥 + 3 2
+ 𝑦 + 1 2
= 4
• 𝑥 − −3
2
+ 𝑦 − −1
2
= 22
• 𝐶 = (−3, −1) 𝑟 = 2

5. • 𝑥 − ℎ 2
+ 𝑦 − 𝑘 2
= 𝑟2
• 𝑥 − (−2) 2
+ 𝑦 − 5 2
= 32
• 𝑥2
+ 4𝑥 + 4 + 𝑦2
− 10𝑦 + 25 = 9
• 𝑥2
+ 𝑦2
+ 4𝑥 − 10𝑦 + 4 + 25 − 9 = 0
• 𝑥2
+ 𝑦2
+ 4𝑥 − 10𝑦 + 20 = 0

6. 𝑥 − ℎ 2
= −4𝑝 𝑦 − 𝑘
𝑝 = 1
𝑉 = (−2, −1) 𝑝 = 1
𝑥 − (−2) 2
= −4 1 𝑦 − −1
𝑥 + 2 2
= −4 𝑦 + 1

7. 𝑦2
− 2𝑦 − 4𝑥 + 13 = 0
𝑉 = (3, 1)
𝐹 = (4, 1)
𝑥 = 2
• 𝑦2
− 2𝑦 = 4𝑥 − 13
• 𝑦 − 1 2
− 1 = 4𝑥 − 13
• 𝑦 − 1 2
= 4𝑥 − 13 + 1
• 𝑦 − 1 2
= 4𝑥 − 12
• 𝑦 − 1 2
= 4 𝑥 − 3

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