Question

What is the radius of the circle with an equation of x2 - 12x + y2 + 4y = -4?

Answer 1

6

Explanation:

h = -12/-2 = 6

k = 4/-2 = -2

h² + k² - r² = 4

6² + (-2)² - 4 = r²

r² = 36

r = sqrt(36) = 6

Answer 2

radius = 6

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 - 12x + y² + 4y = - 4

Using the method of completing the square on the x and y terms

add (half the coefficient of the x/y term )² to both sides

x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = - 4 + 36 + 4, that is

(x - 6)² + (y + 2)² = 36 ← in standard form

with r² = 36 ⇒ r =
`√(36)` = 6