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Find the general equation of the circle with diameter whose endpoints are (3,4) and (1,2)

User Xose Lluis
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Final answer:

The general equation of the circle is (x - 2)^2 + (y - 3)^2 = sqrt(2)

Step-by-step explanation:

The general equation of a circle with diameter whose endpoints are given can be found using the formula:

(x - h)^2 + (y - k)^2 = r^2

First, find the coordinates of the center of the circle using the midpoint formula:

h = (x1 + x2)/2 and k = (y1 + y2)/2

In this case, the endpoints are (3,4) and (1,2), so the center is (2,3).

Next, find the radius by determining the distance between the center and one of the endpoints:

r = sqrt((x2 - h)^2 + (y2 - k)^2)

Substituting the values, the general equation of the circle is:

(x - 2)^2 + (y - 3)^2 = sqrt(2)

User InspectorDanno
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