Answer:
Step-by-step explanation:
Review: the standard equation for a circle with center at (0, 0) and radius r is x² + y² = r².
Thus, x² + y² = 4 has its center at (0, 0) and r² = 4; its radius is √4, or 2. This corresponds to the center described in the first blue answer choice.
Going on to the 2nd blue answer choice:
Let's start out with a review of the standard equation of a circle with center at (h, k) and radius r. It is (x-h)² + (y-k)² = r².
Now if we take the necessary data from the blue answer choice, namely, center at (3, -4) and radius 6, we substitute 3 for h, -4 for k and 6 for r. This gives us
(x-3)² + (y+4)² = 6² = 36, which corresponds to the fourth yellow equation.
Last, we take the third blue specifications: Center at (1, 0) and radius r = 3.
Substituting 1 for h, 0 for k and 3 for r, we get:
(x-1)² + (y-0)² = 3². This is the same as (x-1)² + y² = 3² = 9.
If we expand this, we get x² - 2x + 1 + y² = 9, or x² - 2x + y² = 8. This matches the 2nd yellow answer choice.
