1. è¯æï¼âµç´çº¿l:mx+ny=1ä¸æ¤åC:x^2/a^2+y^2/b^2=1(aï¼bï¼0)交äºä¸å两ç¹
èç«æ¹ç¨å¾ï¼mx+ny=1 â
:x^2/a^2+y^2/b^2=1 â¡
åç®æ´çå¾ï¼ï¼b^2+a^2m^2/n^2ï¼x^2-2a^2m/n^2x+a^2/n^2-a^2b^2=0
ç±æ ¹çå¤å«å¼â³>0å¾4a^4m^2/n^2-4(b^2+a^2m^2/n^2)(a^2/n^2-a^2b^2)>0
åç®å¾(a^2b^4n^2-a^2b^2+a^4b^2m^2)/n^2>0
å 为n^2>0
æ以a^2b^4n^2-a^2b^2+a^4b^2m^2>0
å³a^2b^4n^2+a^4b^2n^2>a^2b^2
ä¹å³a^2m^2+b^2n^2>1
2. è¯æï¼è®¾P(x1,y1),R(x2,y2)
å 为OPâ¥OR
æ以åéOP.åéOR=0
å³x1x2+y1y2=0
ç±é¦è¾¾å®çå¾ x1+x2=2a^2m/(b^2n^2+a^2m^2)
X1.x2=(a^2-a^2b^2n^2)/(b^2n^2+a^2m^2)
带å
¥mx+ny=1å¾ y1.y2=(b^2n^2-a^2b^2n^2m^2)/(b^2n^4+a^2m^2n^2)
â´(a^2-a^2b^2n^2)/(b^2n^2+a^2m^2)+ (b^2n^2-a^2b^2n^2m^2)/(b^2n^4+a^2m^2n^2)=0
å³(a^2+b^2-a^2b^2n^2-a^2b^2m^2)/(b^2n^2+a^2m^2)=0
ä¹å³a^2+b^2=a^2b^2(m^2+n^2)
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