24Its a good question...but radical axis not in syllabus..
I will wait for someone to prove it..otherwise I will do so
Try to prove that the locus of the centre of a circle that cuts two given circles orthogonally is the radical axis of the two given circles.(very important proof in coordinate geometry)
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4 Answers
24
3radical axis is given by S1-S2=0
apply the conditon for orthogonal intersection then the proof comes in the immediate next step.
3well organic y do u rate this is an important proof in coordinate geometry,may be i dunno the usage of the proof.
3let that circle be havin f,g,c as thier std coeff
and the 2 given circles have f1,g1,c1 and f2,g2,c2
2g1g + 2f1f =c1 + c
2f2f + 2g2g = c2 + c
subtract both
2(g1-g2)g + 2(f1-f2)f = c1-c2 ...
rep. g by x and f by y ......we get the locus which is same as S1-S2 or the radicle axis
