Difference between revisions of "2021 AMC 10A Problems/Problem 24"
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| + | ==Problem 24== | ||
| + | The interior of a quadrilateral is bounded by the graphs of <math>(x+ay)^2 = 4a^2</math> and <math>(ax-y)^2 = a^2</math>, where <math>a</math> a positive real number. What is the area of this region in terms of <math>a</math>, valid for all <math>a > 0</math>? | ||
| + | <math>\textbf{(A)} ~\frac{8a^2}{(a+1)^2}\qquad\textbf{(B)} ~\frac{4a}{a+1}\qquad\textbf{(C)} ~\frac{8a}{a+1}\qquad\textbf{(D)} ~\frac{8a^2}{a^2+1}\qquad\textbf{(E)} ~\frac{8a}{a^2+1}</math> | ||
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| + | ==Solution== | ||
Revision as of 23:00, 11 February 2021
Problem 24
The interior of a quadrilateral is bounded by the graphs of 
and 
, where 
a positive real number. What is the area of this region in terms of , valid for all 
?
