Mathematics

Problem

If the tangent to the curve

y = 1 - x^2

x = \alpha

, where

0 < \alpha < 1

, meets the axes at P and Q. As

\alpha

varies, the minimum value of the area of the triangle OPQ is

k

times the area bounded by the axes and the part of the curve for which

0 < x < 1

, then

k

is equal to - (A)

\frac{2}{\sqrt{3}}

(B)

\frac{75}{16}

(C)

\frac{25}{18}

(D)

\frac{2}{3}