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Thread: Need help with a parametrics question

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    New Member impulsebro89's Avatar
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    Need help with a parametrics question

    Hi everyone!

    Will you please help me with this question:

    The points A (−6, -9) and B(u,v) lie on the parabola x^2 =-4ay such that AB is a normal to the parabola at B.
    (i) Find the value of a.
    (ii)Given the roots of x^3 − 28x + 48 = 0 are −6, 2, 4, find the coordinates of B.

    I can't seem to get part (ii).

    Help please! Thanks
    Last edited by impulsebro89; 14 Apr 2018 at 9:42 PM.

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    617 pages fan96's Avatar
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    Re: Interesting parametrics question!

    i)

    Using the general equation of the parabola



    and the given point , we can deduce .

    ii)

    Let be given by



    The cartesian equation of the normal to the parabola is

    .

    Using the coordinates of to substitute in for ,



    Which gives the equation of the normal to the parabola at the point .

    Because we require to be on the normal, we can substitute into the equation and solve for .

    After substitution and simplfication you will get the equation given to you in ii).
    Last edited by fan96; 14 Apr 2018 at 10:09 PM.
    impulsebro89 likes this.
    HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]

    1(3√3) t2 dt cos(3π/9) = log(3√e) | Integral t2 dt, From 1 to the cube root of 3. Times the cosine, of three pi over nine, Equals log of the cube root of e.

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