Results 1 to 7 of 7

Math Help - Find parabola if...

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    18

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    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?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    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.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2009
    Posts
    18
    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.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2009
    Posts
    18
    solved nvm

    thanks
    Last edited by hello; March 27th 2010 at 08:43 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    \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.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Mar 2009
    Posts
    18
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: March 22nd 2011, 04:57 PM
  2. Find the equation of the parabola
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 2nd 2010, 06:50 PM
  3. Find equation of the parabola
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 17th 2010, 11:42 AM
  4. Find Parabola Equation
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 23rd 2008, 09:38 PM
  5. Find parabola equation
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 14th 2008, 02:55 AM

Search Tags


/mathhelpforum @mathhelpforum