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Question

How are the points (1,1),(2,2) and (2,3) situated with respect to the circle x2+y24x2y+3=0

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Solution

Given equation is x2+y2+2x4y3=0
Let A=(1,1),B=(2,2) and C=(2,3)
For point A(1,1),x2+y2+2x4y3=1+1243=7<0
Hence point A lies inside the circle
For point B=(2,2),x2+y2+2x4y3=4+44+83=9>0
Hence point B lies outside the circle
For point C=(2,3),x2+y2+2x4y3=4+94123=6<0
Hence point C lies inside the circle

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