Final Answer:
No, the point (3, 6) does not lie on the circle with radius 6 and center (-2, 3).
Step-by-step explanation:
To determine whether the point (3, 6) lies on the circle, we need to calculate the distance between the point and the center of the circle. If the distance is equal to the radius, then the point lies on the circle. Otherwise, the point does not lie on the circle.
The distance formula tells us that the distance between two points (x1, y1) and (x2, y2) is:
sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the center of the circle is (-2, 3) and the point is (3, 6). Plugging these values into the distance formula, we get:
sqrt((3 - (-2))^2 + (6 - 3)^2)
= sqrt(25 + 9)
= sqrt(34)
Since the radius of the circle is 6, the point (3, 6) does not lie on the circle because the distance between the point and the center is not equal to the radius.