Question 378272
Complete the square in x and y.
{{{x^2 + y^2 + 2x - 4y - 31 = 0 }}}
{{{(x^2+2x)+(y^2-4y)-31=0}}}
{{{(x^2+2x+1)+(y^2-4y+4)-31=1+4}}}
{{{(x+1)^2+(y-2)^2=36}}}
{{{(x+1)^2+(y-2)^2=6^2}}}
The general equation for a circle centered at ({{{h}}},{{{k}}}) with a radius {{{R}}} is:
{{{(x-h)^2+(y-k)^2=R^2}}}
Comparing,
Radius:{{{R=6}}}
Center:({{{h}}},{{{k}}})=({{{-1}}},{{{2}}})
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{{{drawing(300,300, -9,7,-6,10, grid(1),circle(-1,2,0.2),graph(300,300,-9,7,-6,10, 0,2+sqrt(36-(x+1)^2)),graph(300,300, -9,7,-6,10 ,0,2-sqrt(36-(x+1)^2))))}}}