a diameter of a circle has endpoints P(-10, -2) and Q(4,6)
find the center of the circle
find the radius.
write and equation for the circle
To find the center of the circle, we can use the midpoint formula:
Center = ((-10 + 4) / 2, (-2 + 6) / 2)
Center = (-6 / 2, 4 / 2)
Center = (-3, 2)
So, the center of the circle is at (-3, 2).
To find the radius of the circle, we can use the distance formula between the center and one of the endpoints:
Radius = sqrt((-3 - (-10))^2 + (2 - (-2))^2)
Radius = sqrt(7^2 + 4^2)
Radius = sqrt(49 + 16)
Radius = sqrt(65)
So, the radius of the circle is sqrt(65).
Now, the equation for the circle can be written in the standard form:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center of the circle and r is the radius.
Substitute the values we found earlier:
(x + 3)^2 + (y - 2)^2 = 65
Therefore, the equation of the circle is (x + 3)^2 + (y - 2)^2 = 65.