Answer:
r = 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² + 4x - 2y = - 1 ← rearrange the x and y terms together
x² + 4x + y² - 2y = - 1
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(2)x + 4 + y² + 2(- 1)y + 1 = - 1 + 4 + 1
(x + 2)² + (y - 1)² = 4 ← in standard form
with r² = 4 ⇒ r = [tex]\sqrt{4}[/tex] = 2
