touch

Prove that the circles x²+y²+2ux+2vy=0 and x²+y²+2u₁x+2v₁y=0 touch each otehre if u₁v=uv₁

2 Answers

x²+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!

good work bhaiya :P :P :P :P :P :P :P

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