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Find the coordinates of the center of the circle.

 

 Sep 5, 2024
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The coordinates given the circle are not correkt. (Thanks ElectricPavlov!)

 

1. Determination of the slope of the chords between the points AO and BA.

mAO=yAxA=12=0.5mBA=yByaxBxA=213(2)=1

 

2. Determination of the coordinates of the centers of the chords BA and AO.

PBA(xB+xA2,yB+ya2)PBA(3+(2)2,2+12)PBA(2.5,1.5)

PAO(xA+xO2,yA+yO2)PAO(2+02,1+02)PAO(1,0.5)

 

3. Point-direction functions for the center points of the chords BA and AO. The slopes of the function graphs are the negative reciprocals of the slopes of the chords.

fBA(x)=1mBA(xxPBA)+yPBAfBA(x)=11(x(2.5))+1.5fBA(x)=1(x+2.5)+1.5=x+4fAO(x)=1mAO(xxPAO)+yPAOfAO(x)=10,5(x(1))+0.5fAO(x)=2(x+1)+0.5=2x+2.5

 

4. Determine the coordinates of point P by equating the two functions.

x+4=2x+2.5xP=1.5yP=xP+4=1.5+4yP=5.5.P(1.5,5.5)

 

laugh !

 Sep 6, 2024
edited by asinus  Sep 7, 2024
edited by asinus  Sep 7, 2024

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