Answer: (x - 3)² + (y + 0.5)² = 3.25 → [tex](x-3)^2+\bigg(y+\dfrac{1}{2}\bigg)^2=\dfrac{13}{4}[/tex]
Step-by-step explanation:
Concentric means they have the same center but different radii.
The equation of a circle is: (x - h)² + (y - k)² = r² where
- (h, k) is the center of the circle
- r is the radius of the circle
Complete the square to find the center of the circle
x² - 6x + _____ + y² + y + _____ = 1 + ____ + ____
↓ ↓
-6/2 = -3 1/2 = 1/2
Equation: (x - 3)² + (y + 1/2)² = r²
Since the circle passes through point (x, y) = (4, -2), input that into the equation to find r².
(x - 3)² + (y + 1/2)² = r²
(4 - 3)² + (-2 + 1/2)² = r²
(1)² + (-3/2)² = r²
1 + 9/4 = r²
13/4 = r²
Equation: (x - 3)² + (y + 1/2)² = 13/4 → [tex](x-3)^2+\bigg(y-\dfrac{1}{2}\bigg)^2=\dfrac{13}{4}[/tex]
In decimal form: (x - 3)² + (y + 0.5)² = 3.25
