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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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高二數學-圓與直線的關係
Nov 17th 2013, 08:47

直線4x-3y+c=0與x^2+y^2+dx+ey-20=0相切於A(-2,2),求數對(d,e)=?請不要用向量法向量求因尚未學到

Ans:

圓形一點切線方程式為:

0=Ax*x+Ay*y+d*(x+Ax)/2+e*(y+Ay)/2-20

=-2x+2y+d(x-2)/2+e(y+2)/2-20

=(-2-d/2)x+(2+e/2)y+(-d+e-20)

=-4x+3y-c

可以獲得3ㄍ方程式:

d/2+2=4 => d=4

e/2+2=3 => e=2

c=d-e+20

=> (d,e)=(4,2).....ans

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