2022 AMC 12B Problems/Problem 8
Problem
What is the graph of in the coordinate plane?
Solution
Since the equation has even powers of and , let and . Then . Rearranging gives , or . There are two 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 .
Video Solution(1-16)
~~Hayabusa1
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.