Identify type of conic and more

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SUMMARY

The discussion focuses on identifying the type of conic represented by the polar equation e=45/(10+9sin(θ). Participants conclude that the conic is an ellipse. To analyze the conic's properties, such as vertices, foci, directrix, and asymptotes, it is essential to convert the polar equation into Cartesian coordinates. The conversion involves manipulating the equation to express all occurrences of r in terms of r² or r sin(θ).

PREREQUISITES
  • Understanding of polar and Cartesian coordinate systems
  • Familiarity with conic sections, specifically ellipses
  • Knowledge of mathematical manipulation techniques for equations
  • Experience with graphing polar equations
NEXT STEPS
  • Learn how to convert polar equations to Cartesian coordinates
  • Study the properties of ellipses, including vertices and foci
  • Explore the derivation of directrix and asymptotes for conic sections
  • Practice graphing various conic sections using polar coordinates
USEFUL FOR

Students studying conic sections, mathematics educators, and anyone interested in the graphical representation and properties of polar equations.

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Identify type of conic and more...

Homework Statement


Identify the type of conic, find the vertices, the foci, directrix, and asymptotes (if they exist) for the equation e=45/(10+9sin(θ))

Homework Equations


As far as equations I don't know of any to help me find which type of conic, or any characteristics of this.

The Attempt at a Solution


Graphing in polar mode, I find that it is an ellipse.
I think we have to convert it from a polar equation into Cartesian coordinates.
 
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I assume e is what's normally written as r in polar.
Multiply out the equation. Then try rearranging it so that when you square both sides every occurrence of r is either as r2 or as r sinθ.
 

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