Part A:
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is (-2, 4) and the diameter is 6 units. The radius is half of the diameter, so the radius is 6/2 = 3 units.
Plugging in the values into the equation, we get:
(x - (-2))^2 + (y - 4)^2 = 3^2
(x + 2)^2 + (y - 4)^2 = 9
Therefore, the equation of the circle is (x + 2)^2 + (y - 4)^2 = 9.
Part B:
To graph the circle by hand, follow these steps:
1. Plot the center: (-2, 4)
2. Use the radius of 3 units to mark points on the x-axis and y-axis. From the center, move 3 units to the left and right on the x-axis and mark those points. Similarly, move 3 units up and down on the y-axis and mark those points.
3. Connect the points to form a circle.
4. Optionally, label the center and any other relevant points.
Part C:
The domain of the circle is the set of x-coordinates of all points on the circle. In this case, the x-coordinate can vary from -2 - 3 = -5 to -2 + 3 = 1 (considering the center and the radius) because the circle extends 3 units to the left and 3 units to the right of the center.
Therefore, the domain of the circle is -5 ≤ x ≤ 1. To determine the domain, you need to consider the center and the radius of the circle.
Part A: What is the equation of a circle with center (−2, 4) and a diameter of 6 units? Show all necessary steps. (4 points)
Part B: Explain how to graph the circle by hand on the coordinate plane. (3 points)
Part C: What is the domain of the circle? Explain how to determine the domain. (3 points)
1 answer