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Mathematics
Problem
For the two fixed points
F
1
(
0
,
6
)
F_{1}(0,6)
F
1
(
0
,
6
)
and
F
2
(
0
,
−
6
)
F_{2}(0,-6)
F
2
(
0
,
−
6
)
, every point
P
(
x
,
y
)
P(x,y)
P
(
x
,
y
)
satisfies
P
F
1
+
P
F
2
=
18
PF_{1}+PF_{2}=18
P
F
1
+
P
F
2
=
18
. Prove that the equation of the locus is
x
2
45
+
y
2
81
=
1.
\frac{x^{2}}{45}+\frac{y^{2}}{81}=1.
45
x
2
+
81
y
2
=
1.
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