Question

There are four steps for converting the equation x^2+y^2+12x+2y-1=0 into standard form by completing the square. Complete the last step.

Answer 1

(x + 6)² + (y + 1)² = 36 + 1 + 1

Explanation:

using the steps given, we are left with:

x² + 12x + 36 + y² + 2x + 1 = 38

we can factor each term in parentheses:

(x² + 12x + 36) + (y² + 2x + 1) = 36 + 1 + 1

lets start with x² + 12x + 36. we factor by finding 2 numbers that add up to 12 and when multiplied together get 36. the answer is 6. so we can factor:

(x + 6)²

next we factor y² + 2x + 1. the same rules apply, and this number would be 1.

(y + 1)²

we have the following:

(x + 6)² + (y + 1)² = 36 + 1 + 1

to simplify the right side, we add the terms, then square it as well to find the radius of the circle, in which the formula is (x - h)² + (y - k)² = r²

(x + 6)² + (y + 1)² = 38²

(x + 6)² + (y + 1)² = 1444

(x + 6)² + (y + 1)² = √1444

(x + 6)² + (y + 1)² = 38

this is the final form