1good work bhaiya :P :P :P :P :P :P :P
Prove that the circles x2+y2+2ux+2vy=0 and x2+y2+2u1x+2v1y=0 touch each otehre if u1v=uv1
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2 Answers
62x2+y2+2ux+2vy=0
is same as
(x+u)2+(y+v)2=u2+v2
same way, 2nd eqtn is
(x+u1)2+(y+v1)2=u12+v12
Now they will touch each other if the distance of the centers is equal to the sum or difference of the radius!
(u-u1)2+(v-v1)2={√u2+v2 - √u12+v12}2
uu1 + vv1=√u2+v2 √u12+v12
square both sides again!!!!!
(u1v-uv1)2=0
hence proved!
