Center is (-3, -2) and radius is 1
Step-by-step explanation:
- Step 1: Given equation of the circle is x² + 6x + y² + 4y + 12 = 0. Standard form is x² + y² + 2gx + 2fy + c = 0. Center is (-g, -f) and radius is √g² + f² - c. Find g, f and c.
By comparing the 2 equations,
⇒ 2gx = 6x
⇒ 2g = 6
∴ g = 6/2 = 3
⇒ 2fy = 4y
⇒ 2f = 4
∴ f = 4/2 = 2
⇒ c = 12
- Step 2: Find center and radius.
Center = (-g, -f) = (-3, -2)
Radius = √g² + f² - c
= √3² + 2² - 12 = √9 + 4 - 12
= 1
