æ¤åæ¹ç¨ï¼x^2/m+y^2/3 = 1
3x^2 + my^2 - 3m = 0
æ y = x - 1 代å
¥ï¼
(m+3)x^2 - 2mx - 2m = 0
å¨ m>0 (æ¤åæ¹ç¨ï¼å¿
æ m>0) æ¶ï¼å¿
ç¶æ两个解 x1, x2
ä¸ x1+x2 = 2m/(m+3), x1x2 = -2m/(m+3)
AO åç´äº BO
y1/x1 * y2/x2 = -1
(x1-1)/x1 * (x2-2)/x2 = -1
2x1x2 = x1+x2 - 1
-4m/(m+3) = 2m/(m+3) - 1
m = 3/5
追é®
è¿é没æ
追ç(x1, y1), (x2, y2) è¿é½æ¯ç´çº¿ y = x - 1 ä¸çç¹ï¼
y1 = x1 - 1
y2 = x2 - 1
代å
¥ y1y2/x1x2 = -1
(x1-1)(x2-1)/x1x2 = -1
x1x2 - (x1+x2) + 1 = - x1x2
2x1x2 = x1+x2 - 1