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Math Help - The equation of the normal to a curve which is parallel to a given line

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    The equation of the normal to a curve which is parallel to a given line

    this is the question:

    find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x-3=0

    please help me...i dont know how to do..
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  2. #2
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    Quote Originally Posted by mastermin346 View Post
    this is the question:

    find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x-3=0

    please help me...i dont know how to do..
    The gradient of 2y-x-3=0 is 1/2. Therefore the gradient of the required normal is 1/2 therefore the gradient of the tangent is -2. So solve dy/dx = -2 to get the x-coordinate and hence y-coordinate of the required point on the curve. Now you have a point and you have a gradient and therefore you can write down the equation of the normal line.
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  3. #3
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    WRITE it

    Quote Originally Posted by mr fantastic View Post
    The gradient of 2y-x-3=0 is 1/2. Therefore the gradient of the required normal is 1/2 therefore the gradient of the tangent is -2. So solve dy/dx = -2 to get the x-coordinate and hence y-coordinate of the required point on the curve. Now you have a point and you have a gradient and therefore you can write down the equation of the normal line.

    can u write it?it dificult to me.
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  4. #4
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    Quote Originally Posted by mastermin346 View Post
    this is the question:

    find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x-3=0

    please help me...i dont know how to do..
    i am sure you know that the gradient of y=1/2x+3/2 is 1/2

    y=-x^2+2x+3

    \frac{dy}{dx}=-2x+2 ... gradient of tangent

    so gradient of normal will be -\frac{1}{2-2x}

    have it equal to 1/2 . Do you know why ?

    then solve for x , sub into the original equation to get y.

    After that , make use the formula that i gave you in my post tp your other question to get the equation .
    Last edited by mr fantastic; October 9th 2009 at 07:06 AM. Reason: Got moved when I moved the original question.
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  5. #5
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    Quote Originally Posted by mastermin346 View Post
    can u write it?it dificult to me.
    You have spent no more than 8 minutes thinking about what I posted before aksing for more help. You need to spend more time than that thinking about the question and the reply I gave.

    Have you tried doing what I suggested? What don't you understand? Where do you get stuck?
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