Question

Part 3: Use the information provided to write the standard form equation of each circle

7. (x + 8)^2 + (y + 14)^2 = 9
Translated 3 right, 5 down

8. (x + 2)^2 - (y - 8)^2 = 49
Translated 3 right, 2 up

9. (x - 4)^2 + (y - 11)^2 = 25
Translated 3 right, 4 up

Answer 1

7. (x + 5)² + (y + 14)² = 9

8. (x - 1)² + (y - 10)² = 49

9. (x - 7)² + (y - 15)² = 25

Explanation:

7. (x + 8)^2 + (y + 14)^2 = 9

Centre: (-8,-14)

Translated 3 right, 5 down

Centre: (-5,-19)

(x - (-5))² + (y - (-14))² = 9

(x + 5)² + (y + 14)² = 9

8. (x + 2)^2 - (y - 8)^2 = 49

Centre: (-2,8)

Translated 3 right, 2 up

Centre: (1,10)

(x - 1)² + (y - 10)² = 49

9. (x - 4)^2 + (y - 11)^2 = 25

Centre: (4,11)

Translated 3 right, 4 up

Centre: (7,15)

(x - 7)² + (y - 15)² = 25

Answer 2

9.
`\displaystyle (x - 7)^2 + (y - 15)^2 = 25`

8.
`\displaystyle (x - 1)^2 - (y - 10)^2 = 49`

7.
`\displaystyle (x + 5)^2 + (y + 19)^2 = 9`

Step-by-step explanation:

`\displaystyle [x - h]^2 - [y - k]^2 = r^2 → Hyperbola\:Equation \\ [x - h]^2 + [y - k]^2 = r^2 → Circle\:Equation \\ [h, k] → Centre`

According to the equations in the exercises, in the parentheses, ALL NEGATIVE SIGNS give the OPPOSITE terms of what they REALLY are, so be EXTREMELY CAREFUL with your translations:

9. [4, 11]

+ 3 + 4

_____

[7, 15] → (x - 7)² and (y - 15)²

8. [−2, 8]

+ 3 + 2

_____

[1, 10] → (x - 1)² and (y - 10)²

7. [−8, −14]

+ 3 - 5

______

[−5, −19] → (x + 5)² and (y + 19)²

** NOTISE THAT THE RADII NEVER ALTER.

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