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Llana [10]
3 years ago
5

The circle given by : x^2 + y^2 - 6y - 12 = 0 can be written as:

Mathematics
1 answer:
deff fn [24]3 years ago
4 0

Step-by-step explanation:

Given equation of circle is,

{x}^{2}  +  {y}^{2}  - 6y - 12 = 0 \\ by \: compairing \: it \: with \:   \\ {x}^{2}  +  {y}^{2}   + 2gx + 2fy = 0 \: we \: get \\2 g = 0 \: or \: g = 0 \\ 2f=  - 6 \\ or \: f=  - 3 \\ c =  - 12

again the another form of circle is,

{x}^{2}  +  {(y - k)}^{2}  = 21 \\ or \:  {x}^{2}  + {y}^{2}  - 2ky +  {k}^{2}  - 21 = 0 \\ by \: compairing \:it \: with \:  \\ {x}^{2}  +  {y}^{2}   + 2gx + 2fy = 0 \: we \: get  \\ g = 0 \\f =  - k \\ c =  {k}^{2}  - 21

now equating the values of f in both equations,

-k=-3

i.e. k=3

therefore k=3

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2 years ago
<img src="https://tex.z-dn.net/?f=0.6%20%5Csqrt%7B33.54%7D%20" id="TexFormula1" title="0.6 \sqrt{33.54} " alt="0.6 \sqrt{33.54}
ki77a [65]

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Hope this helps!

Thanks!

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3 years ago
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IrinaVladis [17]

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