If P is on the ellipse, and (absolute value of Pf1) - (P It is known that the two focal points of ellipse are F1 (0, - 1) F2 (0,1) eccentricity e = 1 / 2 Find 1. Elliptic equation 2. If P is on the ellipse and (absolute value of Pf1) - (absolute value of PF2) = 1, find the cos angle f1pf2 | Math enthusiast | Mathematical art

If P is on the ellipse, and (absolute value of Pf1) - (P It is known that the two focal points of ellipse are F1 (0, - 1) F2 (0,1) eccentricity e = 1 / 2 Find 1. Elliptic equation 2. If P is on the ellipse and (absolute value of Pf1) - (absolute value of PF2) = 1, find the cos angle f1pf2

According to the meaning of the title
c=1,c/a=1/2
a=2
b²=a²-c²=4-1=3
b=√3
Elliptic equation: Y & sup2 / 4 + X & sup2 / 3 = 1
PF1+PF2=4
PF1-PF2=1
2PF1=5
PF1=5/2
PF2=3/2
Cosine theorem
cosF1PF2=(PF1²+PF2²-F1F2²)/(2PF1*PF2)
=(25/4+9/4-4)/(2×5/2×3/2）
=(25+9-16)/(2×5×3)
=18/30
=3/5

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