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Mathematics
Mathematics
Problem
Let for two distinct values of
p
p
p
the lines
y
=
x
+
p
y = x + p
y
=
x
+
p
touch the ellipse
E
:
x
2
4
2
+
y
2
3
2
=
1
E: \frac{x^2}{4^2} + \frac{y^2}{3^2} = 1
E
:
4
2
x
2
+
3
2
y
2
=
1
at the points
A
A
A
and
B
B
B
. Let the line
y
=
x
y = x
y
=
x
intersect
E
E
E
at the points
C
C
C
and
D
D
D
. Then the area of the quadrilateral
A
B
C
D
ABCD
A
B
C
D
is equal to
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