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7
2000 HMMT RMT Geometry # 7
2000 HMMT RMT Geometry # 7
Source:
March 3, 2024
conics
ellipse
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle inscribed in the ellipse
x
2
4
+
y
2
9
=
1
\frac{x^2}{4} +\frac{y^2}{9}= 1
4
x
2
+
9
y
2
=
1
. If its centroid is the origin
(
0
,
0
)
(0,0)
(
0
,
0
)
, find its area.
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