1
椭圆方程x²/a²+y²/b²=1,
e=c/a=√3/2,
c=√3a/2,
准线x=a²/c
a²/c=4√3/3
a²/(√3a/2)=4√3/3
a=2
c=√3
b=√(a²-c²)=1
x²/4+y²=1
2
F1(√3,0) F2(-√3,0)
F1F2=2√3
PF1+PF2=2a=4
(PF1+PF2)²=16
2PF1PF2=16-PF1²+PF2²
PF1⊥PF2
PF1²+PF2²=F1F2²
PF1²+PF2²=12
2PF1PF2=16-12
PF1PF2=2
△F1PF2的面积=PF1PF2/2=1
3
Q到椭圆距离d²=(x-0)²+(y-3/2)²=x²+(y-3/2)²
x²=4-4y²
d²=4-4y²+(y-3/2)²
d²=-3(y+1/2)²+7
y=-1/2时 d²=7
d最大=√7