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Math Help - Parametric Equations

  1. #1
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    Parametric Equations

    The parametric equations of curve C are

    x=1/t

    y=t

    a) Show that the tangent to C at the point P with parameter p has equation

    y+2px-3p=0

    b) The tangent to the point C at the point P intersects the x-axis at A and the y-axis at B. Show that PB=2PA


    I don't know how to do this question. I know how to find dy/dx but not sure if i need it never attempted one of these questions help pleaase =]
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  2. #2
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    Parametric equations

    Hello djmccabie
    Quote Originally Posted by djmccabie View Post
    The parametric equations of curve C are

    x=1/t

    y=t

    a) Show that the tangent to C at the point P with parameter p has equation

    y+2px-3p=0

    b) The tangent to the point C at the point P intersects the x-axis at A and the y-axis at B. Show that PB=2PA


    I don't know how to do this question. I know how to find dy/dx but not sure if i need it never attempted one of these questions help pleaase =]
    (a) x = \frac{1}{t}\Rightarrow \frac{dx}{dt} = -\frac{1}{t^2}

    y = t^2\Rightarrow \frac{dy}{dt}= 2t

    \Rightarrow \frac{dy}{dx} = 2t \times (-t^2) = -2t^3

    The point P has parameter p; in other words, at P t = p. So at P, x = \frac{1}{p}, y = p^2,\frac{dy}{dx}= -2p^3

    So the tangent at P has equation

    y - p^2 = -2p^3(x - \frac{1}{p})

    = -2p^3x + 2p^2

    i.e. y + 2p^3x - 3p^2 = 0

    (b) This line meets the y-axis at B , where x = 0 and y+0-3p^2=0

    \Rightarrow y = 3p^2 at B.

    So the increase in y from A to P is p^2, and the increase in y from P to B is 2p^2. So by similar triangles, PB = 2PA.

    Grandad
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