Results 1 to 2 of 2

Thread: Parabola - find the equation

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    22

    Parabola - find the equation

    Find the equation of the line tangent to y^2=-16x and parallel to x+y=1.

    Please help me with this or just give me an idea on how to answer this problem... Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by lance View Post
    Find the equation of the line tangent to y^2=-16x and parallel to x+y=1.

    Please help me with this or just give me an idea on how to answer this problem... Thanks!
    If the line is parallel to $\displaystyle x + y = 1$, then its gradient is $\displaystyle 1$. (Why?)


    You want the equation of the tangent that has the same gradient.

    So $\displaystyle y^2 = -16x$

    $\displaystyle \frac{d}{dx}(y^2) = \frac{d}{dx}(-16x)$

    $\displaystyle 2y\,\frac{dy}{dx} = -16$

    $\displaystyle \frac{dy}{dx} = -\frac{8}{y}$.


    So when the gradient is $\displaystyle 1$...

    $\displaystyle -\frac{8}{y} = 1$

    $\displaystyle -\frac{y}{8} = 1$

    $\displaystyle y = -8$.


    When $\displaystyle y = -8$ we have $\displaystyle (-8)^2 = -16x$

    $\displaystyle 64 = -16x$

    $\displaystyle x = -4$.


    So we have the gradient $\displaystyle = 1$ and a coordinate $\displaystyle (-4, -8)$ that lies on the tangent.

    Put this information into $\displaystyle y = mx + c$, solve for the unknown $\displaystyle c$, and then you will have the equation of the tangent.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: Mar 22nd 2011, 04:57 PM
  2. Find the equation of the parabola
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Dec 1st 2010, 06:59 PM
  3. Find the equation for the parabola...
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Apr 8th 2010, 07:01 PM
  4. Find an equation of the parabola?
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: Mar 19th 2010, 12:27 PM
  5. How to find the equation of a Parabola
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Jun 1st 2009, 08:27 PM

Search Tags


/mathhelpforum @mathhelpforum