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Mathematics
Mathematics
Problem
Let the length of a latus rectum of an ellipse
x
2
a
2
+
y
2
b
2
=
1
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
a
2
x
2
+
b
2
y
2
=
1
be 10. If its eccentricity is the minimum value of the function
f
(
t
)
=
t
2
+
t
+
11
12
f(t) = t^2 + t + \frac{11}{12}
f
(
t
)
=
t
2
+
t
+
12
11
,
t
∈
R
t \in \mathbb{R}
t
∈
R
, then
a
2
+
b
2
a^2 + b^2
a
2
+
b
2
is equal to :
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