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Math Help - Help with solving a parabola

  1. #1
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    Help with solving a parabola

    P is the point (ap^2 , 2ap) and Q the point (aq^2 , 2aq) on the parabola y^2 = 4ax. The cord PQ passes through the point (a,0)

    a) Prove that pq = -1

    I have no idea how to get started . Thanks in advance
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  2. #2
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    Re: Help with solving a parabola

    Quote Originally Posted by womatama View Post
    P is the point (ap^2 , 2ap) and Q the point (aq^2 , 2aq) on the parabola y^2 = 4ax. The cord PQ passes through the point (a,0)

    a) Prove that pq = -1

    I have no idea how to get started . Thanks in advance
    Start by drawing a diagram. Have you done that?
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  3. #3
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    Re: Help with solving a parabola

    Quote Originally Posted by womatama View Post
    P is the point (ap^2 , 2ap) and Q the point (aq^2 , 2aq) on the parabola y^2 = 4ax. The cord PQ passes through the point (a,0)

    a) Prove that pq = -1

    I have no idea how to get started . Thanks in advance
    You have 2 points. Determine the equation of the line which passes through these points: If you know P_1(x_1 , y_1) and P_2(x_2 , y_2) then the equation of the line P_1P_2 is:

    \dfrac{y-y_1}{x-x_1}= \dfrac{y_2-y_1}{x_2-x_1}

    Since this line has to pass through (a, 0) you only have to replace x by a and y by 0. Simplify!
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