Answer:
radius = 2 units
Explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
(h, k ) are the coordinates of the centre and r is the radius
given
x² + y² + 8x - 6y + 21 = 0 ( subtract 21 from both sides )
x² + y² + 8x - 6y = - 21 ( collect x/ y terms together )
x² + 8x + y² - 6y = - 21
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(4)x + 16 + y² + 2(- 3)y + 9 = - 21 + 16 + 9
(x + 4)² + (y - 3)² = 4 ← in standard form
with r² = 4 , then
r =
= 2 units