The tangent to the curve at

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The tangent to the curve

y=1-x^2

x=\alpha

, where

0<\alpha<1

, meets the axes at

P

and

Q

. If

\alpha

varies and the minimum area of

\triangle OPQ

k

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

0<x<1

, then

k

is equal to (1)

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

(2)

\frac{75}{16}

(3)

\frac{25}{18}

(4)

\frac{2}{3}