Final answer:
The radius of the circle with the center at (-4,6) that passes through the point (-4,10) is calculated by finding the distance between the two points, which is 4 units.
Step-by-step explanation:
The student's question appears to ask for assistance in finding the radius of a circle with the center at (-4,6) that passes through the point (-4,10). To solve this, we calculate the distance between the center of the circle and the point it passes through. This distance is the radius of the circle. Since both points have the same x-coordinate (-4), we can find the radius by subtracting the y-coordinate of the center from the y-coordinate of the point that lies on the circumference, resulting in:
Radius = |y2 - y1| = |10 - 6| = 4
Therefore, the radius of the circle is 4 units.