A non-straight curve C lies in the first quadrant. At each of its points, the tangent meets the positive coordinate axes at A and B . If O A + OB = 1 , find the minimum distance d of C from the origin

Question

A non-straight curve C lies in the first quadrant. At each of its points, the tangent meets the positive coordinate axes at A and B . If O A + OB = 1 , find the minimum distance d of C from the origin.

TestHub · Accepted Answer

Let the positive intercepts be u , v , with u + v = 1 . The envelope of x / u + y / v = 1 is x ​ + y ​ = 1 . At (1/4, 1/4) the distance is 1/ ( 2 2 ​ ) ; the endpoint limits have distance 1 , so this is the minimum.

Mathematics - Parabola Question with Solution | TestHub

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