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kasse
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How can one find the eq. of an ellipse given that the foci are (-2,0) and (2,0) and that the directrices are x=-8 and x=8?
Finding the equation of an ellipse from foci and directrices
- Thread starter kasse
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- Ellipse
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SUMMARY
The equation of an ellipse can be derived from its foci and directrices. Given foci at (-2,0) and (2,0), and directrices at x=-8 and x=8, the standard form of the ellipse can be established. The distance between the foci is 4, which indicates that the semi-major axis is 2. The directrices provide the necessary parameters to finalize the equation of the ellipse.
PREREQUISITES- Understanding of conic sections, specifically ellipses
- Knowledge of the standard form of an ellipse equation
- Familiarity with the concepts of foci and directrices
- Basic algebra skills for manipulating equations
- Study the derivation of the standard form of an ellipse equation
- Learn about the properties of ellipses, including eccentricity
- Explore examples of finding equations of conic sections from given parameters
- Practice problems involving the calculation of distances between foci and directrices
Students studying precalculus, mathematics educators, and anyone interested in mastering the properties and equations of ellipses.
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