Equation of a Circle
We are given the equation:
[tex]x^2+y^2+10x+12y+12=0[/tex]
The equation of a circle of radius r and center (h,k) is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
To convert the given equation into the standard form, we need to complete squares as follows.
First, rearrange terms:
[tex]x^2+10x+y^2+12y+12=0[/tex]
The term 10x is divided by 2x to find the correct number to complete:
10x/(2x) = 5
Similarly, dividing 12y/(2y) = 6
Now we complete both squares by adding (and subtracting) 25 and 36:
[tex]x^2+10x+25+y^2+12y+36+12-25-36=0[/tex]
Operating:
[tex](x+5)^2+(y+6)^2=49[/tex]
Second choice
