If the tangent to the curve y = 1 - x2 at x = α, where 0

Question

If the tangent to the curve y = 1 - x2 at x = &#945;, where 0 < &#945; < 1 , meets the axes at P and Q. As &#945; 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 -

Accepted Answer

Equation of tangent is y -1+ &#945;2 = - 2&#945;(x - &#945;)so P& Q (0, &#945;2 + 1)area of &#5123; OPQ (&#5123;) = = [&#945;3 + 2&#945; + ]&#5123;&#8242; = [3&#945;2 + 2 - ] = 0&#8658; 3&#945;4 + 2&#945;2 - 1 = 0 &#8658; &#945; = so &#5123; = Now (1 - x2)dx&#8658; &#8658;

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