Question

The equation for a circle is ​x2+10x+y2+12y+52=0​ .

Answer 1

I believe the answer is (x+5)^2+(y+6)^2=9

Answer 2

Equation of circle in standard form is $(x-h)^{2} + (y-k)^{2} =r^{2}$

where (h,k) is the center of the circle and r is the radius.

To write the given equation in standard form we take 52 to the other side .The equation we have is :

$x^{2} +10x +y^{2} + 12y =-52$

To complete the square we take half of coefficient of x and y terms then square it .This is added to both sides of the equation .Half the coefficient of x term is 5 and half the coefficient of y term is 6 .Squaring it we have $5^{2} and 6^{2}$

Adding this to both sides:

$x^{2} +10x + 5^{2} +y^{2} +12y + 6 ^{2} = -52 +5^{2} + 6^{2}$

Simplifying we have:

$(x+5)^{2} +(y+6) ^{2} =9$

The last option is the right answer.