Results 1 to 2 of 2

Thread: Parabola QUestion

  1. #1
    Newbie
    Joined
    Jan 2006
    Posts
    20

    Parabola QUestion

    The question goes:

    Find the y-intercept of the normal to the parabola y=x^2 at the point
    (a,a^2), where a cannot equal 0. Find the limit of this y-interept as a approaches 0. For each b>0 determine the number of normals that can be drawn from the point (0,b) to the parabola y=x^2; justify your answer.

    So far i have gotton that the y intercepts= 1/2+a^2, however, i'm not sure what the limit of the y intercept as a approaches 0. Additionally, i can't figure out how to determine the amount of normals.

    Thanks a Lot

    Willie Li
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, aussiekid90!

    Find the y-intercept of the normal to the parabola $\displaystyle y = x^2$
    at the point $\displaystyle (a,a^2)$, where $\displaystyle a \neq 0$

    (a) Find the limit of this y-intercept as $\displaystyle a \to 0$.

    You did the hard work . . . You found that the y-intercept is: .$\displaystyle \frac{1}{2} + a^2$

    As $\displaystyle a\to0$, we see that $\displaystyle \left(\frac{1}{2} + a^2\right) \to \frac{1}{2}$



    (b) For each $\displaystyle b>0$, determine the number of normals that can be drawn
    from the point $\displaystyle (0,b)$ to the parabola $\displaystyle y=x^2$.

    We already know that the y-intercept is: .$\displaystyle b \:=\:a^2 + \frac{1}{2}$
    . . Then:. $\displaystyle a \:=\:\pm\sqrt{b - \frac{1}{2}} $

    In general, for every $\displaystyle b$, there are two values of $\displaystyle a$.


    Therefore, there are two normals that can be drawn . . .
    except: when $\displaystyle b = \frac{1}{2}$, then one normal can be drawn
    . . and when $\displaystyle b < \frac{1}{2}$ when there are no normals.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Parabola question
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Jun 6th 2010, 12:45 PM
  2. Parabola Question
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: Jun 14th 2009, 06:16 PM
  3. parabola question
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Mar 28th 2009, 06:42 PM
  4. Parabola(?) Question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Jan 20th 2009, 02:03 AM
  5. A Question About a Parabola
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Nov 19th 2006, 06:52 AM

Search Tags


/mathhelpforum @mathhelpforum