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2021 AMC 10A Problem 24

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2021 AMC 10A Problem 24AMC 10 Step by Step
Name:                             Date: September 13, 2026
Coordinate Geometry · difficulty 4 of 5 · about 6 min · position P21-25

The interior of a quadrilateral is bounded by the graphs of (x+ay)2=4a2(x+ay)^2 = 4a^2 and (ax−y)2=a2(ax-y)^2 = a^2 , where aa is a positive real number. What is the area of this region in terms of aa , valid for all a>0a > 0 ?

  1. A)

    8a2(a+1)2\frac{8a^2}{(a+1)^2}

  2. B)

    4aa+1\frac{4a}{a+1}

  3. C)

    8aa+1\frac{8a}{a+1}

  4. D)

    8a2a2+1\frac{8a^2}{a^2+1}

  5. E)

    8aa2+1\frac{8a}{a^2+1}

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