Deriving Standard Form of Ellipse Equation

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SUMMARY

The discussion focuses on the derivation of the standard form of the ellipse equation, emphasizing the importance of reversibility in mathematical operations. Participants clarify that squaring both sides of an equation does not introduce extraneous solutions when only the positive square root is taken. The consensus is that as long as both sides are positive, the derivation remains valid, ensuring that the equality holds true without introducing contradictions.

PREREQUISITES
  • Understanding of basic algebraic operations
  • Familiarity with the properties of square roots
  • Knowledge of the standard form of conic sections
  • Basic principles of mathematical reversibility
NEXT STEPS
  • Study the derivation of the standard form of conic sections, specifically ellipses
  • Learn about the implications of squaring equations in algebra
  • Explore the properties of square roots and their applications in equations
  • Investigate common pitfalls in mathematical derivations and how to avoid them
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Students of mathematics, educators teaching conic sections, and anyone interested in understanding the derivation and properties of the ellipse equation.

Mahmoud2010
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in the derivation of the standard form of equation of ellipse

[PLAIN]http://img694.imageshack.us/img694/8324/capturedpw.jpg

we squared both sides of equation isn't that means that we have produce we have produced a candidate which doesn't satisfy the original equation.

Thanks
 
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There is no problem because all of your steps are reversible. When you work the steps in reverse order, the only place where there is a potential problem is where you take square roots. But if you look carefully, you will see that you are only taking the positive square root of both sides, which themselves are positive numbers. And if you have two positive numbers a and b with a2=b2, then a = b. You don't have the possibility that a = ±b.
 
I think of this also . but I want to be more certain.

At all Thanks for help.
 

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