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geometry 03' #17

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i've already read the soln from joint-us but i don't think the soln's arguement is strong enough please do bii) with clear steps (as detailed as possible) (i can't see why Q is vertically below M)

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先設定三條方程式:C1,C2同FG 2007-11-14 17:35:06 補充: 設r1及r2分別為C1及C2的半徑得出C1:x^2+(y-r1)^2=r1^2C2:(x-p)^2+(y-r2)^2=r2^2FG:y=b 2007-11-14 17:41:27 補充: 解C1及FG,得x=±√[r1^2-(b-r1)^2]其中x=√[r1^2-(b-r1)^2]就是M的x座標,即√[r1^2-(b-r1)^2]=a而x=-√[r1^2-(b-r1)^2]就是F的x座標,即F(-√[r1^2-(b-r1)^2],b) 2007-11-14 17:46:46 補充: 所以F(-a,b)解C2及FG,得x=p±√[r2^2-(b-r2)^2]其中x=p-√[r2^2-(b-r2)^2]就是M的x座標,即√[r2^2-(b-r2)^2]=a而x=p+√[r2^2-(b-r2)^2]就是G的x座標,即G(p+√[r2^2-(b-r2)^2,b)所以G(2p-a,b) 2007-11-14 18:01:01 補充: 然後,定出FQ和GQ方程式由點F(-a,b)及原點(0,0)得FQ:ay=-bx由點G(2p-a,b)及點P(p,0)得GQ:(p-a)y=bx-bp解FQ同GQx=ay=-b得Q(a,-b) 2007-11-14 18:02:07 補充: 更正其中x=p-√[r2^2-(b-r2)^2]就是M的x座標,即√[r2^2-(b-r2)^2]=a為其中x=p-√[r2^2-(b-r2)^2]就是M的x座標,即p-√[r2^2-(b-r2)^2]=a

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