Note: Your teacher will grade your response to this question to ensure you receive proper credit for your answer. A diameter of a circle has endpoints P(–10, –2) and Q(4, 6). Find the center of the circle. Find the radius. If your answer is not an integer, express it in radical form. Write an equation for the circle. (3 points)
To find the center of the circle, we first need to find the midpoint of the diameter, which can be calculated by taking the average of the x-coordinates and y-coordinates of the endpoints.
Midpoint:
x-coordinate: (–10 + 4) / 2 = –6 / 2 = –3
y-coordinate: (–2 + 6) / 2 = 4 / 2 = 2
Therefore, the center of the circle is at point C(–3, 2).
Next, we find the radius by calculating the distance from the center to one of the endpoints using the distance formula:
r = √[(x2 - x1)^2 + (y2 - y1)^2]
r = √[(-3 - (-10))^2 + (2 - (-2))^2]
r = √[7^2 + 4^2]
r = √[49 + 16]
r = √65
Therefore, the radius of the circle is √65.
Finally, the equation of the circle can be written as:
(x + 3)^2 + (y - 2)^2 = 65
simplify it and make it like a human wrote it
To find the center of the circle, we first find the midpoint of the diameter by averaging the x-coordinates and y-coordinates of the endpoints:
Midpoint:
x-coordinate: (-10 + 4) / 2 = -6 / 2 = -3
y-coordinate: (-2 + 6) / 2 = 4 / 2 = 2
So, the center of the circle is at C(-3, 2).
Next, we find the radius by calculating the distance from the center to one of the endpoints using the distance formula:
r = √[(-3 - (-10))^2 + (2 - (-2))^2]
r = √[7^2 + 4^2]
r = √[49 + 16]
r = √65
Thus, the radius of the circle is √65.
Finally, the equation of the circle can be written as:
(x + 3)^2 + (y - 2)^2 = 65.