What are the standard form, radius, and center?

Question

The equation of a circle is $x^{2} + y^{2} - 4 x + 2 y - 11 = 0$ $x^2+y^2-4x+2y-11=0$ .

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Answer 1 · 2018-05-21T19:36:59

r=4

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Answer 2 · 2018-05-21T19:40:55

Standard form ${(x - 2)}^{2} + {(y + 1)}^{2} = 16$ $(x-2)^2+(y+1)^2=16$
Radius is 4
Centre (2,-1)

$x^{2} - 4 x + y^{2} + 2 y = 11$ $x^2-4x+y^2+2y=11$

Complete the square

${(x - 2)}^{2} - 4 + {(y + 1)}^{2} - 1 = 11$ $(x-2)^2-4+(y+1)^2-1=11$

${(x - 2)}^{2} + {(y + 1)}^{2} = 16$ $(x-2)^2+(y+1)^2=16$

${(x - 2)}^{2} + {(y + 1)}^{2} = 4^{2}$ $(x-2)^2+(y+1)^2=4^2$