Monday, December 24, 2012

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 60

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=(53)2+(7(1))2dPQ=(8)2+(8)2dPQ=64+64dPQ=82 units


Therefore, the radius is..

r=dPQ2=822=42 units

Also, recall that the general equation for the circle with circle (h,k) and
radius r is..


(xh)2+(yk)2=r2Model(xh)2+(yk)2=(42)2Substitute the given(xh)2+(yk)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=352=1

Thus, the equation of the circles..


(x3)2+(y(1))2=32(x3)2+(y+1)2=32

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