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Mathematics
Mathematics
Problem
A line passing through the point
P
(
5
,
5
)
P(\sqrt{5}, \sqrt{5})
P
(
5
,
5
)
intersects the ellipse
x
2
36
+
y
2
25
=
1
\frac{x^2}{36} + \frac{y^2}{25} = 1
36
x
2
+
25
y
2
=
1
at
A
A
A
and
B
B
B
such that
(
P
A
)
⋅
(
P
B
)
(PA) \cdot (PB)
(
P
A
)
⋅
(
P
B
)
is maximum. Then
5
(
P
A
2
+
P
B
2
)
5(PA^2 + PB^2)
5
(
P
A
2
+
P
B
2
)
is equal to :
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