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.

Answer 1

The answer is :

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

Answer 2

We want to convert into standard form, the equation
x² + y² + 12x + 2y - 1 = 0

Note that
(x + a)² = x² + 2ax + a²
so that
x² + 2ax = (x + a)² - a²

Therefore
x² + y² + 12x + 2y - 1 = 0
x² + 12x + y² + 2y = 1
(x + 6)² - 6² + (y + 1)² - 1² = 1
(x + 6)² + (y + 1)² - 37 = 1
(x + 6)² + (y + 1)² = 38

Theis equation represents a circle with center at (-6, -1) and radius √(38), as shown below.

Answer: (x + 6)² + (y + 1)² = 38