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Mathematics
Problem
Let
F
1
(
0
,
−
c
)
F_1(0,-c)
F
1
(
0
,
−
c
)
and
F
2
(
0
,
c
)
F_2(0,c)
F
2
(
0
,
c
)
be two points with
c
>
a
>
0
c>a>0
c
>
a
>
0
. Show that the locus of a point
P
(
x
,
y
)
P(x,y)
P
(
x
,
y
)
satisfying
∣
P
F
2
−
P
F
1
∣
=
2
a
|PF_2-PF_1|=2a
∣
P
F
2
−
P
F
1
∣
=
2
a
is
y
2
a
2
−
x
2
c
2
−
a
2
=
1.
\frac{y^2}{a^2}-\frac{x^2}{c^2-a^2}=1.
a
2
y
2
−
c
2
−
a
2
x
2
=
1.
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