å·²ç¥æ²çº¿x^2+y^2+x-6y+3=0ä¸ä¸¤ç¹PãQ满足ï¼â å
³äºç´çº¿kx-y+4=0对称ï¼â¡OPâ¥OQãæ±ç´çº¿PQçæ¹ç¨ã
é¢ç®ç»çæ¯åçä¸è¬æ¹ç¨x^2+y^2+x-6y+3=0 â
âµåçæ²çº¿ä¸ä¸¤ç¹PãQå
³äºç´çº¿kx-y+4=0对称
â´ç´çº¿kx-y+4=0è¿åå¿(-1/2,3)
â´k=2
设ç´çº¿PQçæ¹ç¨ä¸º:y=-1/2x+b â¡
â â¡èç«å¾5/4 x^2+(4-b)x+b^2-6b+3=0
设P(x1,y1)ãQ(x2,y2)
âµOPâ¥OQ
â´OPåé·OQåé=0
â´x1x2+y1y2=0
â´x1x2+(-1/2x1+b)(-1/2x2+b)=0
x1x2+1/4 x1x2-1/2b(x1+x2)+b^2=0
åâµx1x2=(b^2-6b+3)/(5/4)
x1+x2=(b-4)/(5/4)
代å
¥åç®å¾8b^2-22b+15=0
解å¾b=3/2æ5/4
â´ç´çº¿PQçæ¹ç¨ä¸ºx+2y-3=0æ2x+4y-5=0
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