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2022 AIME Problems
12
conics ew
conics ew
Source: 2022 AIME II Problem 12
February 17, 2022
AMC
AIME
AIME II
Problem Statement
Let
a
,
b
,
x
,
a, b, x,
a
,
b
,
x
,
and
y
y
y
be real numbers with
a
>
4
a>4
a
>
4
and
b
>
1
b>1
b
>
1
such that
x
2
a
2
+
y
2
a
2
−
16
=
(
x
−
20
)
2
b
2
−
1
+
(
y
−
11
)
2
b
2
=
1.
\frac{x^2}{a^2}+\frac{y^2}{a^2-16}=\frac{(x-20)^2}{b^2-1}+\frac{(y-11)^2}{b^2}=1.
a
2
x
2
+
a
2
−
16
y
2
=
b
2
−
1
(
x
−
20
)
2
+
b
2
(
y
−
11
)
2
=
1.
Find the least possible value of
a
+
b
.
a+b.
a
+
b
.
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