A non-straight curve C in the first quadrant has tangents meeting the positive axes at A , B . If each intercepted segment A B has length 1, find its minimum distance d from the origin.

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TestHub · Accepted Answer

For u 2 + v 2 = 1 , the envelope of x / u + y / v = 1 is the first-quadrant astroid x 2/3 + y 2/3 = 1 . Its closest point is x = y = 1/ ( 2 2 ​ ) , at distance d = 1/2 .

Mathematics - Application of Derivative Question with Solution | TestHub

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