圓心在直線Y=3X上,圓心C(a,3a)
(x-a)^2+(y-3a)^2=r^2
圓C被Y軸截得的弦長為2√2
x=0,a^2+(y-3a)^2=r^2
y=3a±√(r^2-a^2)
|y1-y2|=2√(r^2-a^2)=2√2
r^2=2+a^2
Y=X與圓C相切
(x-a)^2+(y-3a)^2=2+a^2
(x-a)^2+(x-3a)^2=2+a^2
2x^2-8ax+9a^2-2=0
△=0
(-8a)^2-4*2*(9a^2-2)=0
a=±√2
r^2=2+a^2=4
圓的方程:
(x±√2)^2+(y±3√2)^2=4