perplexus.info :: Geometry : Getting Quadratic and Cubic with Astroid

Getting Quadratic and Cubic with Astroid (Posted on 2011-10-22)

The respective lengths of the perpendiculars drawn from the origin to the tangent and to the normal of the astroid x^2/3 + y^2/3 = a^2/3 are denoted by F and G.

Determine all possible real a that satisfy this relationship:

4*F² + G² = a³ – 18.

Submitted by K Sengupta

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Solution: (Hide)

The only real solution is a = 3.

For a detailed explanation, refer to the solution submitted by Harry in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Solution	K Sengupta	2012-03-21 09:53:05
Solution	Harry	2011-10-24 23:31:45

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