Question

complete the square with the following equation of a circle so that you can convert the equation into standard form.

Answer 1

Equation of a Circle

We are given the equation:

`x^2+y^2+10x+12y+12=0`

The equation of a circle of radius r and center (h,k) is:

`(x-h)^2+(y-k)^2=r^2`

To convert the given equation into the standard form, we need to complete squares as follows.

First, rearrange terms:

`x^2+10x+y^2+12y+12=0`

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:

`x^2+10x+25+y^2+12y+36+12-25-36=0`

Operating:

`(x+5)^2+(y+6)^2=49`

Second choice