An ellipse frac{(x-x_0)^2}{a^2} + frac{(y-y_0 | vedclass

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(C) Since the ellipse is tangent to both axes in the first quadrant,its center is $(a, b)$. The foci are $(a \pm ae, b)$ or $(a, b \pm ae)$. Given the

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$\frac{1}{2}$

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(C) Since the ellipse is tangent to both axes in the first quadrant,its center is $(a, b)$. The foci are $(a \pm ae, b)$ or $(a, b \pm ae)$. Given the geometry,the center is $(a, b)$ and the distance from the origin to the center is $\sqrt{a^2 + b^2}$.For an ellipse tangent to the axes,$x_0 = a$ and $y_0 = b$. The foci are $(a \pm ae, b)$.Given $	riangle OF_1F_2$ is isosceles with $\angle OF_1F_2 = 120^{\circ}$,we have $OF_1 = F_1F_2 = 2ae$.Using the law of cosines in $	riangle OF_1F_2$ or coordinate geometry properties,we find $e = \frac{1}{2}$.

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