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    The point P(at^2 , 2at) lies on the parabola C with equation y^2 = 4ax, where a is a positive constant. The tangent to C at P is ty = x + at^2

    The tangent to C at the point A and the tangent to C at the point B meet at the point with coordinated (-4a,3a).

    Find in terms of a, the coordinates of A and the coordinates of B
    anyone know where to start with this question?
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    The first thing to do would be draw a diagram detailing what you know. You should then be able to work from the point of intersection to find your points A and B, as these are the only points of intersections of the tangent lines with C.
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    (Original post by doin' your mum)
    The point P(at^2 , 2at) lies on the parabola C with equation y^2 = 4ax, where a is a positive constant. The tangent to C at P is ty = x + at^2

    The tangent to C at the point A and the tangent to C at the point B meet at the point with coordinated (-4a,3a).

    Find in terms of a, the coordinates of A and the coordinates of B
    anyone know where to start with this question?
    Create the equation of tangent line in form of
    y=m(x+4a)+3a
    where m is the gradient parameter
    Solve this and the y^2=4ax equations simultaneously.
    Take the discriminant of quadratic equation you got for x equal with zero because the line will tangent if there will be on solution for x, that is one common point with the parabola.
    This give you 2 values for m. From these gradients and the derivative of
    the parabola you can determine the coordiantes of A and B on the parabola.
 
 
 
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