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Math Help - Ellipse chord joining two points subtends an angle identity can't understand the Ques

  1. #1
    Member ssadi's Avatar
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    Ellipse chord joining two points subtends an angle identity can't understand the Ques

    Show that an equation of the chord joining the points P (acos\omega, bsin\omega) and Q (acos\theta, b sin\theta) on the ellipse with equation b^2x^2+a^2y^2=a^2b^2 is
    Bxcos\frac{1}{2}(\theta+\omega)+aysin{1}{2}(\theta  +\omega)=abcos{1}{2}(\theta-\omega)<br />
(SOLVED)

    “Prove that, if the chord PQ subtends a right angle at the point (a,0), then PQ passes through a fixed point on the x-axis.”
    The part in the quotation, I cannot understand what it demands, let alone do it. Will be gratified if somebody comes forward with a more graphic explanation. Help
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  2. #2
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    Quote Originally Posted by ssadi View Post
    ...

    “Prove that, if the chord PQ subtends a right angle at the point (a,0), then PQ passes through a fixed point on the x-axis.”
    The part in the quotation, I cannot understand what it demands, let alone do it. Will be gratified if somebody comes forward with a more graphic explanation. Help
    I've attached a sketch of the situation. I've marked two different right angles at (a,0). All together there are drawn 11 right angles.

    As you can see all chords intersect in one point on the x-axis. You are asked to calculate the coordinates of this point.

    For the sketch I used a = 6, b = 4
    Attached Thumbnails Attached Thumbnails Ellipse chord joining two points subtends an angle identity can't understand the Ques-rectwinkl_ellips.png  
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  3. #3
    Member ssadi's Avatar
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    Quote Originally Posted by earboth View Post
    I've attached a sketch of the situation. I've marked two different right angles at (a,0). All together there are drawn 11 right angles.

    As you can see all chords intersect in one point on the x-axis. You are asked to calculate the coordinates of this point.

    For the sketch I used a = 6, b = 4
    Is there any program you used, or did you do it by hand?
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  4. #4
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    Quote Originally Posted by ssadi View Post
    Is there any program you used, or did you do it by hand?
    Google for Geogebra

    The program is free-ware.
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