Difference between revisions of "2012 AMC 12B Problems/Problem 10"
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==Problem== | ==Problem== | ||
− | What is the area of the polygon whose vertices are the points of intersection of the curves <math>x^2 + y^2 =25 and (x-4)^2 + 9y^2 = 81 ?</math> | + | What is the area of the polygon whose vertices are the points of intersection of the curves <math>x^2 + y^2 =25</math> and <math>(x-4)^2 + 9y^2 = 81 ?</math> |
==Solution== | ==Solution== |
Revision as of 12:04, 26 January 2014
Problem
What is the area of the polygon whose vertices are the points of intersection of the curves and
Solution
The first curve is a circle with radius 5 centered at the origin, and the second curve is an ellipse with center (4,0) and end points of (-5,0) and (13,0). Finding points of intersection, we get (-5,0) (4,3) and (4,-3), forming a triangle with height of 9 and base of 6. So 9x6x0.5 =27 ; B.
See Also
2012 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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 |
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