Final answer:
To graph Circle T on a coordinate plane, the center is at the origin (0, 0) and the radius is found by calculating the distance between the center and a given point on the circle. The radius is √13. The equation of Circle T is x² + y² = 13.
Step-by-step explanation:
To graph Circle T on a coordinate plane, we need to know the coordinates of its center and the length of its radius. We are given that the center of Circle T is at the origin (0, 0) and it passes through Point P (-3, 2). So, the center of the circle is (0, 0) and the radius can be found by calculating the distance between the center (0, 0) and Point P (-3, 2) using the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Plugging in the values, we get:
Distance = √((-3 - 0)² + (2 - 0)²) = √((-3)² + 2²) = √(9 + 4) = √13
So, the radius of Circle T is √13.
The equation of Circle T can be found using the standard form of the equation of a circle, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
In this case, the equation of Circle T would be x² + y² = (√13)² or x² + y² = 13.