Parametric Equations for an Ellipse

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SUMMARY

The discussion focuses on deriving parametric equations for the ellipse represented by the rectangular equation \(\frac{(y-2)^2}{49} - \frac{(x-1)^2}{9} = 1\). The ellipse is centered at (1, 2) with semi-major axis 7 and semi-minor axis 3. Participants compare this to the unit circle equation \(x^2 + y^2 = 1\) and seek a simpler understanding of the parametrization process. A hint involving trigonometric identities is provided to facilitate comprehension.

PREREQUISITES
  • Understanding of parametric equations
  • Familiarity with ellipse geometry
  • Basic knowledge of trigonometric identities
  • Ability to manipulate algebraic equations
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  • Study the derivation of parametric equations for ellipses
  • Learn about the properties of ellipses and their geometric significance
  • Explore trigonometric identities and their applications in parametrization
  • Investigate the relationship between ellipses and circles in coordinate geometry
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Students in mathematics, educators teaching geometry, and anyone interested in understanding parametric equations and their applications in conic sections.

metking92
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Write a pair of parametric equations for the figure whose rectangular equation is
((y-2)^2)/49)-((x-1)^2)/9)=1


please help me
 
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Compare it to the equation x^2+y^2=1 which is almost the same. Does this equation look familiar? Do you what kind of geometric figure it represents? Can you find a parametrization for this simplified problem?
 
Hi i am sorry but i still don't understand this. Is there anyway you can make it simpler.
 
metking92 said:
Hi i am sorry but i still don't understand this. Is there anyway you can make it simpler.

Here is a clue

if sin2x+cos22=1

and you divide throughout by cos2x, what do you get?
 

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