Final answer:
The two circles have centers 10.44 units apart; without knowing their radii, we can't conclude whether they intersect or touch, but we know their relative position in the Cartesian plane.
Step-by-step explanation:
Based on the description, the two circles have their centers at (-7, -5) for the top circle and (3, -2) for the bottom circle. To determine the relationship between these circles, it's important to analyze their centers. The first step might be to calculate the distance between the two centers, which can be found using the distance formula √((x2-x1)² + (y2-y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two centers. For our circles, plug in the coordinates to get the distance: √((3 - (-7))² + ((-2) - (-5))²) = √(100 + 9) = √109, which is approximately 10.44 units.
Without additional context, such as the radii of the circles, we cannot conclude whether they are touching, intersecting, or separate from each other, but we can say that their centers are 10.44 units apart. If the circles were to have radii that sum to more than 10.44 units, then they would intersect. If the sum of their radii were exactly 10.44 units, they would be tangent to each other. If the sum of their radii were less than 10.44 units, the circles would not touch.