16.
令\(\displaystyle \tan\theta=k,\tan\frac{\theta}{2}=t\),\( \displaystyle O_1(\frac{y_1}{t},y_1),O_2(\frac{y_2}{t},y_2)\)
把P代到圓,\( \displaystyle (2-\frac{y}{t})^2+(2-y)^2=y^2 \),整理得\( \displaystyle \frac{y^2}{t^2}+(...)y+8 = 0\)
兩根之積:\(y_1y_2=r_1r_2=2\)就可以知道\( \displaystyle t=\frac{1}{2}\),再二倍角回去就好
計算1,令\( B(x,y) \),\(\displaystyle \frac{y}{x+\frac{9}{2}}\times \frac{y}{x+2}=-1\),\( \displaystyle x^2+\frac{13}{2}x+9+y^2 = 0\),橢圓整理成\(\displaystyle \frac{5}{9}x^2+y^2=5\)
相減求出\(\displaystyle x=-12或-\frac{21}{8}\),-12不合,代回橢圓求出\(\displaystyle y = \pm\frac{5\sqrt{3}}{8}\)(正不合)
[ 本帖最後由 BambooLotus 於 2025-3-8 08:10 編輯 ]