Find the equation of a ellipse given the foci. (1,0) (3,4)

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SUMMARY

The equation of an ellipse cannot be determined solely from the foci located at (1,0) and (3,4). An additional parameter, specifically the minor radius, is required to define the ellipse completely. The foci provide essential information, but without the minor radius, multiple ellipses can fit the same foci. Therefore, to find a unique equation, both the foci and the minor radius must be specified.

PREREQUISITES
  • Understanding of ellipse properties and definitions
  • Knowledge of coordinate geometry
  • Familiarity with the standard form of an ellipse equation
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Research the standard form of an ellipse equation and its components
  • Learn how to calculate the distance between foci and vertices of an ellipse
  • Explore the relationship between the foci, major axis, and minor axis
  • Study examples of finding ellipse equations given different parameters
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Students studying conic sections, mathematics educators, and anyone interested in geometry and the properties of ellipses.

Mary89
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Find the equation of a ellipse given the foci. (1,0) (3,4)
 
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You should provide some workings to show what you have tried. What properties about ellipses and their foci do you know?
 
The locations of the foci are not enough to determine the ellipse. You also need to specify an additional parameter, say the minor radius, which can be any positive number.
 

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