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  1. March 26th 2010, 04:55 PM #1
    hello
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    Arrow Find parabola if...

    Q: Find the equation of the parabola if its tangent line at x=2 is

    y=\frac{2}{\sqrt{3}}x-\frac{\sqrt{3}}{3}


    TYIA
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  2. March 26th 2010, 06:51 PM #2
    skeeter
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    Quote Originally Posted by hello View Post
    Q: Find the equation of the parabola if its tangent line at x=2 is

    y=\frac{2}{\sqrt{3}}x-\frac{\sqrt{3}}{3}
    There are quite a few parabolas that will work ... is there more information? what do the instructions for this exercise say?
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  3. March 27th 2010, 03:42 AM #3
    HallsofIvy
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    Quote Originally Posted by hello View Post
    Q: Find the equation of the parabola if its tangent line at x=2 is

    y=\frac{2}{\sqrt{3}}x-\frac{\sqrt{3}}{3}


    TYIA
    At x= 2 y= \sqrt{3} so you are asking for a parabola that passes through (2,\sqrt{3}) and has derivative \frac{2}{\sqrt{3}} there. As skeeter says, there are an infinite number of such parabolas. Even if we restrict to parabolas with vertical axis, there are an infinite number of answers.
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  4. March 27th 2010, 06:25 AM #4
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    Oops, I did leave out some info. Sorry, hehe I kinda started off in the middle of the question.

    Original q: Find equation of a parabola which is tangent to this curve

    y=\sqrt{x^2-1} at x=2

    so yeah this


    was just the tang. line I found for the given function.
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  5. March 27th 2010, 08:25 AM #5
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    solved nvm

    thanks
    Last edited by hello; March 27th 2010 at 08:43 AM.
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  6. March 27th 2010, 08:50 AM #6
    skeeter
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    \sqrt{x^2-1} = ax^2+bx+c at x = 2

    derivatives ...

    \frac{x}{\sqrt{x^2-1}} = 2ax + b

    ... are also equal at x = 2.

    since the question said "a" parabola, let c = 0.

    get two equations in terms of a and b and solve the system for the coefficients.
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  7. March 27th 2010, 10:02 AM #7
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    Thanks, yeah I realised I had to do something like that so I took the even easier route of letting b=0 and therefore finding a and c.
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