wolframalphaは、ブラウザieだと調子が悪いので、firefoxをおすすめします。
(参考)点から円への接点を求める
https://qiita.com/tydesign/items/5ce4bd2cc58902606895
(参考)sympyで円と円の交点
https://qiita.com/mrrclb48z/items/fca16b65c9186954fedc
【例】中心(3,2) 半径 5 の円に対して、点 (15,5) から引いた２つの接線の接点を求める。
方法1:全部変数
Solve[{(x-x0)^2+(y-y0)^2=r^2,(x-x1)^2+(y-y1)^2=(x0-x1)^2+(y0-y1)^2-r^2},{x,y}]
https://ja.wolframalpha.com/input/?i=Solve%5B%7B%28x-x0%29%5E2%2B%28y-y0%29%5E2%3Dr%5E2%2C%28x-x1%29%5E2%2B%28y-y1%29%5E2%3D%28x0-x1%29%5E2%2B%28y0-y1%29%5E2-r%5E2%7D%2C%7Bx%2Cy%7D%5D
結果:
解けたみたい(表示省略)
方法2:連立方程式６つ
Solve[{(x-x0)^2+(y-y0)^2-r^2==0,(x-x1)^2+(y-y1)^2-(x0-x1)^2-(y0-y1)^2+r^2==0,x0==3,y0==2,r==5,x1==15,y1==5},{x,y}]
https://ja.wolframalpha.com/input/?i=Solve%5B%7B%28x-x0%29%5E2%2B%28y-y0%29%5E2-r%5E2%3D%3D0%2C%28x-x1%29%5E2%2B%28y-y1%29%5E2-%28x0-x1%29%5E2-%28y0-y1%29%5E2%2Br%5E2%3D%3D0%2Cx0%3D%3D3%2Cy0%3D%3D2%2Cr%3D%3D5%2Cx1%3D%3D15%2Cy1%3D%3D5%7D%2C%7Bx%2Cy%7D%5D
結果:
x≈3.8516 ∧ y≈6.92694
x≈6.06997 ∧ y≈-1.94655
方法3:連立方程式2つ
(x-3)^2+(y-2)^2=5^2,(x-15)^2+(y-5)^2=(3-15)^2+(2-5)^2-5^2
https://ja.wolframalpha.com/input/?i=%28x-3%29%5E2%2B%28y-2%29%5E2%3D5%5E2%2C%28x-15%29%5E2%2B%28y-5%29%5E2%3D%283-15%29%5E2%2B%282-5%29%5E2-5%5E2
結果:
x≈3.8516, y≈6.92694
x≈6.06997, y≈-1.94655
方法4:方法1に,座標の値を代入する方法
？誰か教えて下さい。
失敗1:実行結果:次をお試しください：
Solve[{(x-x0)^2+(y-y0)^2==r^2,(x-x1)^2+(y-y1)^2==(x0-x1)^2+(y0-y1)^2-r^2,x0==3,y0==2,r==5,x1==15,y1==5},{x,y}]
https://ja.wolframalpha.com/input/?i=Solve%5B%7B%28x-x0%29%5E2%2B%28y-y0%29%5E2%3D%3Dr%5E2%2C%28x-x1%29%5E2%2B%28y-y1%29%5E2%3D%3D%28x0-x1%29%5E2%2B%28y0-y1%29%5E2-r%5E2%2Cx0%3D%3D3%2Cy0%3D%3D2%2Cr%3D%3D5%2Cx1%3D%3D15%2Cy1%3D%3D5%7D%2C%7Bx%2Cy%7D%5D
失敗2:実行結果:次をお試しください：
Solve[{(x-x0)^2+(y-y0)^2=r^2,(x-x1)^2+(y-y1)^2=(x0-x1)^2+(y0-y1)^2-r^2=0,x0=3,y0=2,r=5,x1=15,y1=5},{x,y}]
https://ja.wolframalpha.com/input/?i=Solve%5B%7B%28x-x0%29%5E2%2B%28y-y0%29%5E2%3Dr%5E2%2C%28x-x1%29%5E2%2B%28y-y1%29%5E2%3D%28x0-x1%29%5E2%2B%28y0-y1%29%5E2-r%5E2%3D0%2Cx0%3D3%2Cy0%3D2%2Cr%3D5%2Cx1%3D15%2Cy1%3D5%7D%2C%7Bx%2Cy%7D%5D