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Math Help - Range of Hyperbolas with the same Foci

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    Question Range of Hyperbolas with the same Foci

    I have multiple hyperbolas sharing the same foci with gradually increasing vertices and eccentricity inside of a compass (see attached thumbnail). At the big degree markers (10, 20, 30, etc.) there are corresponding hyperbolas. I would like to be able to have have an equation the can graph all possible hyperbolas down to a tenth of a degree. What is the best way to get a nice range of curves?
    Attached Thumbnails Attached Thumbnails Range of Hyperbolas with the same Foci-fig13-1-1-.jpg  
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