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Thread: Parametrics Question

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    Parametrics Question

    Parabola: x^2 = 8y
    a) show that the equation of a line through the point (3,-2) with gradient m is given by mx - y - 3m - 2 = 0

    b) Show that if a line through (3,-2) with gradient m is a tangent to the parabola
    x^2 =8y then 64m^2 - 96m - 64 = 0

    c) Find the two points A and B on x^2 = 8y where the tangents from (3,-2) meet the parabola x^2 = 8y

    d) show that AB is a focal chord


    Does someone mind helping me with this q. Also idk what part c and d are asking
    thnx

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    Re: Parametrics Question

    a) Use the point gradient formula.



    b) Solve simultaneously the equations of the parabola and line. You'll end up with one big equation.

    Use:
    1. the observation that if the line is tangent to the parabola, there is only one solution to that equation, and
    2. the properties of the discriminant

    c) If you haven't already, draw a diagram. Two lines passing through the point (-3, 2) are tangents to the parabola. You are asked to find where these lines touch the parabola. Part b) sets you up to answer this question.

    d) A focal chord is one that passes through the focus of a parabola. Use the condition of a focal chord for the parameters and of points and .
    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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