1994 Putnam A2

Let $A$ be the area of the region in the first quadrant bounded by the

line $y = \frac{1}{2} x$, the $x$-axis, and the ellipse $\frac{1}{9} x^2

+ y^2 = 1$. Find the positive number$m$such that$A$ is equal to the

area of the region in the first quadrant bounded by the line $y = mx$,

the $y$-axis, and the ellipse $\frac{1}{9} x^2 + y^2 = 1$.

设 $A$ 为第一象限中由

线 $y = \frac{1}{2} x$、$x$ 轴和椭圆 $\frac{1}{9} x^2

+ y^2 = 1$。找到正数$m$使得$A$ 等于

由线 $y = mx$ 界定的第一象限区域的面积，

$y$ 轴和椭圆 $\frac{1}{9} x^2 + y^2 = 1$。