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Math Help - AS exam question

  1. #1
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    AS exam question

    Another question from me.


    The curve C has equation y=x^2(x-6) + \frac{4}{x}, x>0.

    The Points P and Q lie on C and have x-coordinates 1 and 2 respectively.

    a) Show that the length of PQ is \sqrt 170.
    b) Show that the tangents to C at P and Q are parallel.
    c) Find an equation for the noram to C at p giving your answer in the form ax +by+c = 0

    No idea where to start with this equation the + \frac{4}{x} on the end really confuses me too, haven't seen that before.
    Last edited by Ifailatmaths; January 8th 2009 at 01:43 PM.
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  2. #2
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    Quote Originally Posted by Ifailatmaths View Post
    Another question from me.


    The curve C has equation y=x^2(x-6) + \frac{4}{x}, x>0.

    The Points P and Q lie on C and have x-coordinates 1 and 2 respectively.

    a) Show that the length of PQ is \sqrt 170.
    b) Show that the tangents to C at P and Q are parallel.
    c) Find an equation for the noram to C at p giving your answer in the form ax +by+c = 0

    No idea where to start with this equation the + \frac{4}{x} on the end really confuses me too, haven't seen that before.
    (a) Substitute the given values of x to get the y-coordinates of P and Q. Then use the distance formula.

    (b) Find dy/dx and calculate its value at x = 1 and x = 2. What do you notice and therefore conclude ...? (To get the derivative, you should note that \frac{4}{x} = 4 x^{-1}).

    (c) From (b) you know the gradient of the tangent. The gradient of the normal is -1/(gradient of tangent). From (a) you have a known point on the tangent. Use these two things to get the equation of the tangent as you would any line.
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