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Thread: Help with Conics & Parametrics

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    Help with Conics & Parametrics

    Whats the difference?
    latex.png FullSizeRender (1).jpg

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    Hi Φ Rathin's Avatar
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by Commando007 View Post
    Whats the difference?
    latex.png FullSizeRender (1).jpg
    The first one is the equation of chord of contact to an ellipse from a point T(x0,y0).
    The second one is an equation of the chord from points P(acosθ,bsinθ) and Q(acosφ,bsinφ) in an ellipse
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    Re: HSC 2017 MX2 Marathon

    How do we get this equation
    File_000 (1).jpeg

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by Commando007 View Post
    How do we get this equation
    File_000 (1).jpeg
    It's most instructive for you to prove these yourself so I will just provide some hints.

    Consider the forms of sin(X+Y), sin(X-Y), cos(X+Y), cos(X-Y) upon expansion. Is it possible to combine these to obtain products of the form sin(X)cos(Y), sin(X)sin(Y), cos(X)cos(Y) ?

    Now choose X and Y appropriately to put these equations in a "sums to products" form.

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by Rathin View Post
    The first one is the equation of chord of contact to an ellipse from a point T(x0,y0).
    The second one is an equation of the chord from points P(acosθ,bsinθ) and Q(acosφ,bsinφ) in an ellipse
    What is the equation of PQ?
    the first image or the second one?

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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by Rathin View Post
    The first one is the equation of chord of contact to an ellipse from a point T(x0,y0).
    The second one is an equation of the chord from points P(acosθ,bsinθ) and Q(acosφ,bsinφ) in an ellipse

    Couldn't the first one also be the equation of the tangent to an ellipse given point that lies on it (x0,y0)

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    Off until 10th JULY dan964's Avatar
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    Re: HSC 2017 MX2 Marathon

    Quote Originally Posted by tsoliman1 View Post
    Couldn't the first one also be the equation of the tangent to an ellipse given point that lies on it (x0,y0)
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