Answer:
The center of the circle is (-2 , 3) ⇒ 3rd answer
Step-by-step explanation:
The equation of a circle is (x - h)² + (y - k)² = r², where
∵ The equation of the circle is x² + 4x + y² - 6y = 12
- Lets make a completing square for x² + 4x
∵ x² = (x)(x)
∵ 4x ÷ 2 = 2x
- That means the second term of the bracket (x + ...)² is 2
∴ The bracket is (x + 2)
∵ (x + 2)² = x² + 4x + 4
∴ We must add 4 and subtract 4 in the equation of the circle
∴ (x² + 4x + 4) - 4 + y² - 6y = 12
Lets make a completing square for y² - 6y
∵ y² = (y)(y)
∵ -6y ÷ 2 = -3y
- That means the second term of the bracket (y + ....) is -3
∴ The bracket is (y - 3)
∵ (y - 3)² = y² - 6y + 9
∴ We must add 9 and subtract 9 in the equation of the circle
∴ (x² + 4x + 4) - 4 + (y² - 6y + 9) - 9= 12
Now lets simplify the equation
∵ (x + 2)² + (y - 3)² - 13 = 12
- Add 13 to both sides
∴ (x + 2)² + (y - 3)² = 25
- Compare it with the form of the equation of the circle to
find h and k
∵ (x - h)² + (y - k)² = r²
∴ h = -2 and k = 3
The center of the circle is (-2 , 3)
