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Mathematics
Mathematics
Problem
For the ellipse
x
2
16
+
y
2
9
=
1
\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1
16
x
2
+
9
y
2
=
1
with foci
S
1
(
−
7
,
0
)
S_{1}(-\sqrt7,0)
S
1
(
−
7
,
0
)
and
S
2
(
7
,
0
)
S_{2}(\sqrt7,0)
S
2
(
7
,
0
)
, let
P
(
t
,
3
4
16
−
t
2
)
P(t,\,\tfrac{3}{4}\sqrt{16-t^{2}})
P
(
t
,
4
3
16
−
t
2
)
be any point on the ellipse (
∣
t
∣
≤
4
|t|\le 4
∣
t
∣
≤
4
). Show that
P
S
1
+
P
S
2
=
8
PS_{1}+PS_{2}=8
P
S
1
+
P
S
2
=
8
.
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