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Math Help - Equations of tangents through point (curve)

  1. #1
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    Equations of tangents through point (curve)

    Determine the exact equations of the tangents to the curve which pass through point P

    curve = (8-x)^(1/2)
    point = 5,2

    I'd like to see how you would solve this. What I tried to do is set the variables of the point as: a, (8-a^(1/2))
    and the slope would be
    -1 /( 2(8-x)^(1/2) )

    Is this right? Putting this into the y-y0 = m (x-x0) seems to get messy...
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    Hello,

    Quote Originally Posted by theowne View Post
    Determine the exact equations of the tangents to the curve which pass through point P

    curve = (8-x)^(1/2)
    point = 5,2

    I'd like to see how you would solve this. What I tried to do is set the variables of the point as: a, (8-a^(1/2))
    and the slope would be
    -1 /( 2(8-x)^(1/2) )

    Is this right? Putting this into the y-y0 = m (x-x0) seems to get messy...
    Your post is already messy

    f'(x)=\frac{-1}{2(8-x)^{1/2}} \quad \leftarrow \quad \text{Right !}

    You want it at the point (5,2), that is to say x=5.

    Find f'(5)


    Then, the equation of the tangent is :

    y=f'(5)(x-5)+\underbrace{f(5)}_{=2}

    Is it more clear ?
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