Question

There are four steps for converting the equation x2 + y2 + 12x + 2y – 1 = 0 into standard form by completing the square. complete the last step. group the x terms together and the y terms together, and move the constant term to the other side of the equation. x²+ 12x + y²+ 2y = 1 determine (b ÷ 2)2 for the x and y terms. (12 ÷ 2)2 = 36 and (2 ÷ 2)2 = 1 add the values to both sides of the equation. x2 + 12x + 36 + y2 + 2y + 1 = 1 + 36 + 1 write each trinomial as a binomial squared, and simplify the right side. (x + )2 + (y + )2 =

Answer 1

Let's first write each step of the procedure:
 Step 1: 
 group the x terms together and the terms and together, and move the constant term to the other side of the equation:
 x² + 12x + y² + 2y = 1
 Step 2:
 determine (b ÷ 2) 2 for the x and y terms.
 (12 ÷ 2) 2 = 36
 and
 (2 ÷ 2) 2 = 1
 Step 3:
 add the values to both sides of the equation.
 x2 + 12x + 36 + y2 + 2y + 1 = 1 + 36 + 1
 Step 4:
 write each trinomial to binomial squared, and simplify the right side.
 (x + 6) 2 + (y + 1) 2 = 38
 Answer:
 the last step is:
 (x + 6) 2 + (y + 1) 2 = 38

Answer 2

The four steps for converting the equation ara:

• Group the x terms together and the y terms together and move the constant term to the other side of the equation

• Complete the square of the function in parenthesis:
• Add the constant values to both sides

• Simplify the right-hand side:

Equation of a circle:

The standard form of writing equation of a circle is expressed as:

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

Given the equation of a circle expressed as

$x^2 + y^2 + 12x + 2y - 1 = 0$

Step 1: Group the x terms together and the y terms together and move the constant term to the other side of the equation

$x^2+12x+y^2+2y=0+1\\(x^2+12x)+(y^2+2y)=1$

Step 2: Complete the square of the function in parenthesis:

$(x^2+12x+(12/2)^2-(12/2)^2)+(y^2+2y+(2/2)^2-(2/2)^2) =1\\(x^2+12x+6^2-6^2)+(y^2+2y+1-1) = 1\\(x+6)^2-36+(y+1)^2-1=1$

Step 3: Add the constant values to both sides

$(x+6)^2+(y+1)^2=1+36+1$

Step 4: Simplify the right-hand side:

$(x+6)^2+(y+1)^2=38$

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