Final answer:
Two equations represent concentric circles if they have the same center but different radii. Match the pairs by looking at the standard form of a circle's equation and comparing the center points and radii.
Step-by-step explanation:
To match pairs of equations that represent concentric circles, one must first understand what an equation of a circle looks like in the standard form. The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2. Two circles are concentric if they share the same center but have different radii. Therefore, when looking at pairs of equations, you need to find the ones where the (h, k) values are the same but the r^2 values differ.
For example:
- Circle 1 equation: (x - 3)^2 + (y + 2)^2 = 4
- Circle 2 equation: (x - 3)^2 + (y + 2)^2 = 9
These equations represent concentric circles centered at (3, -2) with radii 2 and 3, respectively.
Remember that not all pairs will be concentric. Disregard equations with different centers or any information that isn't part of the equation of the circle.