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tatuchka [14]
3 years ago
7

Help center of circle

Mathematics
1 answer:
Lelu [443]3 years ago
7 0

Answer:

Center = (7, - 5)

Radius = 3

Step-by-step explanation:

{x}^{2}  +  {y}^{2}  + 14x - 10y + 65 = 0 \\  {x}^{2}  + 14x +  {y}^{2}  - 10 + 65 = 0 \\ ( {x}^{2}  + 14x +  {7}^{2})  -  {7}^{2}  +  ({y}^{2}  - 10y +  {5}^{2})  \\-  {5}^{2}  + 65 = 0 \\ (x + 7)^{2}  + (y - 5)^{2}  - 49 - 25 + 65 = 0 \\  (x + 7)^{2}  + (y - 5)^{2}  - 49  + 40= 0 \\   (x + 7)^{2}  + (y - 5)^{2}  - 9= 0 \\   (x + 7)^{2}  + (y - 5)^{2}   =  9 \\  (x + 7)^{2}  + (y - 5)^{2}   =   {3}^{2}  \\  equating \: it \: with \: \\ (x  -  h)^{2}  + (y - k)^{2}   =   {r}^{2}  \\  - h = 7 \implies \: h =  - 7 \\  - k =  - 5 \implies \: k = 5 \\ center = ( - h, \:  - k)  = (7, \:  \:  - 5) \\  \\ radius \: r = 3

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