To find the center of the circle, we need to find the midpoint of the diameter. We can use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Plugging in the coordinates of P and Q:
Midpoint = ((-10 + 4)/2, (-2 + 6)/2) = (-3, 2)
So the center of the circle is (-3, 2).
To find the radius, we can use the distance formula between the center and one of the endpoints of the diameter (e.g. P):
radius = distance(P, center)
= √((x2 – x1)^2 + (y2 – y1)^2)
= √((-3 – (-10))^2 + (2 – (-2))^2)
= √(49 + 16)
= √65
So the radius is √65.
To write the equation of the circle, we can use 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. Plugging in the values we found:
(x – (-3))^2 + (y – 2)^2 = (√65)^2
Simplifying:
(x + 3)^2 + (y – 2)^2 = 65
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.
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