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Question

Find the equation to the circle which passes through the points(1,1)(2,2) and whose radius is 1. Show that there are two such circles.

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Solution

(xh)2+(yx)2=x2passingthroughpoint(1,1)4(2,2)radius(x,y)=(1,1)(2,2)(1h)2+(1k)2=12...........(1)(2h)2+(2k)2=12...........(2)(1h)2+(1k)2=(2h)2+(2k)212h+h2+12x+x2=h4h+h2+hk(x)2+2h+2k=6h+k=3...........(3)h=3k.........(12)(1(3k))2+(1k)2=1(k2)2+(1k)2=1k2+44k+1+k22k=12t26k+4=0k23k+2=0(k2)(k1)=0k=2,k=1fork=2h=32=1k=1,h=31=2for(h,k)=(2,1):(x2)2+(y1)2=12(x2)2+(y1)2=12..........(3)for(h.k)=(1,2)(x1)2+(y2)2=12

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