Difference between revisions of "2022 AMC 12B Problems/Problem 8"
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== See also == | == See also == | ||
{{AMC12 box|year=2022|ab=B|num-b=7|num-a=9}} | {{AMC12 box|year=2022|ab=B|num-b=7|num-a=9}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 13:49, 9 December 2022
Problem
What is the graph of in the coordinate plane?
Solution 1
Since the equation has even powers of and
, let
and
. Then
. Rearranging gives
, or
. There are 2 cases:
or
.
If , taking the square root of both sides gives
, and rearranging gives
. Substituting back in
and
gives us
, the equation for a circle.
Similarly, if , we take the square root of both sides to get
, or
, which is equivalent to
, a hyperbola.
Hence, our answer is .
See also
2022 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.