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. x^2 + y^2 + 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 (-2,1). (type an ordered pair.) the radius of the circle is r =

Explanation:

Step1: Recall circle standard - form

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

Step2: Identify $r^2$ value

We are given the standard - form equation $(x + 2)^2+(y - 1)^2=36$. Since $r^2 = 36$.

Step3: Calculate the radius

Take the square root of $r^2$. So, $r=\sqrt{36}=6$.

Answer:

$6$