Question

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

x2 + 6x + y2 - 4y = 10

Answer 1

Answer: center = (-3, 2) radius = √23

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((6)/(2)\bigg)^2+y^2-4y+\bigg((-4)/(2)\bigg)^2 = 10 +\bigg((6)/(2)\bigg)^2+\bigg((-4)/(2)\bigg)^2\\\\\\(x+3)^2+(y-2)^2=23\\\\\\\rightarrow (h,k)=(-3,2)\\\\\rightarrow r^2=23\quad \rightarrow r=√(23)`