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Thread: Sketching Ellipses + Hyperbolas

  1. #1
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    Exclamation Sketching Ellipses + Hyperbolas

    Hello.

    Could someone please explain to me how to do the parts regarding the angle x??? (I've already sketched the ellipse, hyperbola + common auxillary circles.)

    Sketch the ellipse $\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2}=1$, the hyperbola $\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2}=1$and their common auxillary circles $\displaystyle x^2 + y^2 = a^2$ and $\displaystyle x^2 + y^2 = b^2$ on the same diagram, showing the angle x and the related points P(acosx, bsinx) - a point in the 1st quadrant on the ellipse - and Q (asecx, btanx) - a point on the hyperbola. Show clearly how the positions of P and Q are determined by the value of x where 0<x<90 degrees.
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  2. #2
    MHF Contributor

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    It's not at all clear what you are asking. You appear to be using "x" with two different meanings.
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  3. #3
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    Exclamation

    Oops. So sorry!

    Sketch the ellipse , the hyperbola and their common auxillary circles and on the same diagram, showing the angle $\displaystyle \theta $and the related points P(acos$\displaystyle \theta $, bsin$\displaystyle \theta $) - a point in the 1st quadrant on the ellipse - and Q (asec$\displaystyle \theta $, btan$\displaystyle \theta $) - a point on the hyperbola. Show clearly how the positions of P and Q are determined by the value of $\displaystyle \theta $ where 0<$\displaystyle \theta $<90 degrees.
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  4. #4
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    Hmmm so I've found how to situate the point P on the diagram but im still stuck with Q. Any help please?
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