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docker41 [41]
3 years ago
8

17

Mathematics
1 answer:
xz_007 [3.2K]3 years ago
3 0

Answer:

Center =  \boxed{1}, \: \boxed{ - 2} \: ; \: Radius =  \boxed{3}

Step-by-step explanation:

{x}^{2}  +  {y}^{2}  - 2x + 4y - 4 = 0 \\  \\  ({x}^{2}  - 2x + 1 - 1) + ( {y}^{2}  + 4y + 4 - 4) - 4 = 0 \\  \\ ( {x}^{2}  - 2x + 1) + ( {y}^{2}  + 4y + 4) - 9 = 0 \\  \\  {(x - 1)}^{2}  +  {(y + 2)}^{2}  = 9 \\  \\ {(x - 1)}^{2}  +  {(y + 2)}^{2}  =  {3}^{2}  \\  \\ equating \: it \: with \\  \\  {(x - h)}^{2}  +  {(y - k)}^{2}  =  {r}^{2}  \\  \\ h = 1 \\ k =  - 2 \\ r = 3 \\  \\ center =  \boxed{1} \: \boxed{ - 2} \:  \: radius =  \boxed{3}

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