设椭圆中心为原点O,一个焦点为F(0,1),长轴和短轴的长度之比为2：1 求椭圆方程设经过原点且斜率

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2a/2b=2:1
a=2bc^2=a^2-b^2=3b^2
c=1,b^2=1/3 a^2=4/3
焦点在y轴y^2/(4/3)+x^2/(1/3)=1
3y^2+12x^2=4
y=tx3t^2x^2+12t^2x^2=4
x^2=4/(3t^2+12t^2)
y^2=4t^2/(3t^2+12t^2)
OQ^2=x^2+y^2=4(t^2+1)/(3t^2+12t^2)
OP^2=OQ^2*（2√3)^2=12*4(t^2+1)/(3t^2+12t^2)
Px^2+Py^2=(t^2+1)Px^2
Px^2=48/(3t^2+12t^2)
Px=4√3/√(3t^2+12t^2)
Py=4√3t/√(3t^2+12t^2)