Results 1 to 2 of 2
Like Tree1Likes
  • 1 Post By fan96

Thread: Need help with a parametrics question

  1. #1
    New Member impulsebro89's Avatar
    Join Date
    Jun 2017
    HSC
    2018
    Gender
    Male
    Posts
    24
    Rep Power
    2

    Need help with a parametrics question

    Hi everyone!

    Will you please help me with this question:

    The points A (−6, -9) and B(u,v) lie on the parabola x^2 =-4ay such that AB is a normal to the parabola at B.
    (i) Find the value of a.
    (ii)Given the roots of x^3 − 28x + 48 = 0 are −6, 2, 4, find the coordinates of B.

    I can't seem to get part (ii).

    Help please! Thanks
    Last edited by impulsebro89; 14 Apr 2018 at 9:42 PM.

  2. #2
    617 pages fan96's Avatar
    Join Date
    May 2017
    HSC
    2018
    Gender
    Male
    Location
    NSW
    Posts
    414
    Rep Power
    2

    Re: Interesting parametrics question!

    i)

    Using the general equation of the parabola



    and the given point , we can deduce .

    ii)

    Let be given by



    The cartesian equation of the normal to the parabola is

    .

    Using the coordinates of to substitute in for ,



    Which gives the equation of the normal to the parabola at the point .

    Because we require to be on the normal, we can substitute into the equation and solve for .

    After substitution and simplfication you will get the equation given to you in ii).
    Last edited by fan96; 14 Apr 2018 at 10:09 PM.
    impulsebro89 likes this.
    HSC 2018: English Adv. [80] • Maths Ext. 1 [98] • Maths Ext. 2 [95] • Chemistry [87] • Software Design [95]

    ATAR: 97.40 | Uni Course: B Advanced Mathematics (Hons) / B Engineering (Hons) (Computer) at UNSW

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •