Question

Determine and state the coordinates of the center and the length of the radius of a circle whose equation is

Answer 1

Answer:  center = (-3, 2)   radius = √23

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²

where center = (h, k) and radius = r

Complete the square for both x and y:

$x^2+6x+\bigg(\dfrac{6}{2}\bigg)^2+y^2-4y+\bigg(\dfrac{-4}{2}\bigg)^2 = 10 +\bigg(\dfrac{6}{2}\bigg)^2+\bigg(\dfrac{-4}{2}\bigg)^2\\\\\\(x+3)^2+(y-2)^2=23\\\\\\\rightarrow (h,k)=(-3,2)\\\\\rightarrow r^2=23\quad \rightarrow r=\sqrt{23}$