(1)
圓1:(x-1)^2+y^2=2 ①
圓心O(1,0),
以O(shè)P為直徑作圓2:(x+1/2)^2+(y+1/2)^2=5/2 ②
設(shè)圓1與圓2交點(diǎn)為Q1,Q2
顯然PQ1,PQ2與圓1相切.PQ1,PQ2就是待求切線.
①②聯(lián)立,可得:
3x-3/4+y+1/4=3x+y-1/2=1/2 => y=1-3x
(x-1)^2+(1-3x)^2=2
10x^2-8x=0
x=0或x=4/5
x=0時(shí),y=1,切線方程為:(y-1)/x=-2/(-2)=1,y=1+x
x=4/5時(shí),y= -7/5,切線方程為:(y+1)/(x+2)=-2/5/(14/5)=-1/7,
x+7y+9=0
綜上所述,切線方程為y=1+x和x+7y+9=0
(2) 設(shè)夾角為s
sin(s/2)=2^0.5 / 10^0.5 = 1/5^0.5
s = 2 arcsin(1/5^0.5)=arcsin(4/5)