Question

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

What is the equation of the circle in standard form?


(x+25)2+(y+36)2=36

(x+5)2+(y+6)2=36

(x+25)2+(y+36)2=9

(x+5)2+(y+6)2=9

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.