Question

Find the center and radius of the circle

Answer 1

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`{x}^(2) - 6x + {y}^(2) - y = 2`

Add sides 9 + 1 / 4

`{x}^(2) - 6x + {y}^(2) - y + 9 + (1)/(4) = 2 + 9 + (1)/(4) \\`

`({x}^(2) - 6x + 9) + ( {y}^(2) - y + (1)/(4) ) = 11 + (1)/(4) \\`

`({x - 3})^(2) + ({y - (1)/(2) })^(2) = (44)/(4) + (1)/(4) \\`

`({x - 3})^(2) + ( {y - (1)/(2) })^(2) = (45)/(4) \\`

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Remainder :

`({x - a})^(2) + ({y - b})^(2) = {R}^(2)`

`center = ( \: a \: , \: b \: )`

`radiuc = R`

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Compare :

`({x - a})^(2) + ( {y - b})^(2) = {R}^(2)`

`( {x - 3})^(2) + ({y - (1)/(2) })^(2) = ({ ( √(45) )/(2) })^(2) \\`

Thus ;

`center = ( \: 3 \: , \: (1)/(2) \: ) \\`

`radius = ( √(45) )/(2) = ( √(9 * 5) )/(2) = (3 √(5) )/(2) \\`

Done...

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