Question

complete the square and write the given equation in standard form. then give the center and radius of the circle and graph the equation. x² + y² + 4x - 2y - 31 = 0 the equation of the circle in standard form is (x + 2)² + (y - 1)² = 36. (simplify your answer.) the center of the circle is . (type an ordered pair.)

Explanation:

Step1: Recall the standard - form of a circle equation

The standard - form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Identify $h$ and $k$ from the given standard - form equation

The given standard - form equation is $(x + 2)^2+(y - 1)^2=36$. Comparing it with $(x - h)^2+(y - k)^2=r^2$, we have $x+2=x - (- 2)$ and $y - 1=y - 1$. So, $h=-2$ and $k = 1$.

Answer:

$(-2,1)$