Answer:
Last option, center (- 8, - 4) and the radius of 7 units
Step-by-step explanation:
The formula for the equation of a circle is (x - h)² + (y - k)² = r², where the center is represented by ordered pair (h, k) and r represents the radius (in units).
First, we can find the radius. If r = radius and in the original equation, r² = 49, we can square root both sides and solve for r:
r² = 49
√(r²) = √49
r = 7
The radius is 7 units long. All of the answer options include this so we continue.
Next, we find the center. In the original equation, the subtraction operations (-) are now addition operations, indicating that the negative that original stood was distributed to each term. Therefore, in order to bring it back, we must factor out a negative 1 (-1) from each of the constants in variables h and k's spots.
(x + 8)² + (x + 4)² = 49
[x - 1(-8)]² + [y - 1(-4)]² = 49
(x - (-8))² + (y - (-4))² = 49
h = -8 and k = -4, therefore the center of the circle is at ordered pair (-8, -4).
This aligns with the last option of the given choices.