Find an equation of the circle with endpoints of a diameter at P(−1,3) and Q(7,−5).
Recall that the diameter is twice the radius so by getting the distance between the points using distance formula,
dPQ=√(−5−3)2+(7−(−1))2dPQ=√(−8)2+(8)2dPQ=√64+64dPQ=8√2 units
Therefore, the radius is..
r=dPQ2=8√22=4√2 units
Also, recall that the general equation for the circle with circle (h,k) and
radius r is..
(x−h)2+(y−k)2=r2Model(x−h)2+(y−k)2=(4√2)2Substitute the given(x−h)2+(y−k)2=32
To get the center (h,k), we get the midpoint of the endpoints of the diameter PQ
h=−1+72=3 and k=3−52=−1
Thus, the equation of the circles..
(x−3)2+(y−(−1))2=32(x−3)2+(y+1)2=32
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