Question

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Answer 1

The equation in the given standard form is $(x+10)^2+(y+6)^2=5^2$

Equation of a circle

The standard equation of a circle is expressed as:

$(x-a)^2+(y-b)^2=r^2$

Given the equation $x^2 + y^2 + 20x + 12y + 111 =0$

Group the function to have:

$(x^2 +20x)+(y^2+ 12y) + 111 =0$

Complete the squares to have:

$(x^2 +20x)+(y^2+ 12y) + 111 =0\\(x^2+20x+10^2-10^2)+(y^2+12y+6^2-6^2)+111=0\\(x+10)^2+(y+6)^2 -100-36+111=0\\(x+10)^2+(y+6)^2-25=0\\(x+10)^2+(y+6)^2=25\\(x+10)^2+(y+6)^2=5^2$

Hence the equation in the given standard form is $(x+10)^2+(y+6)^2=5^2$

Learn more on equation of a circle here: brainly.com/question/1506955