Results 1 to 2 of 2

Thread: Prove tangent bisects line

  1. #1
    Senior Member
    Jul 2009

    Prove tangent bisects line

    P is a point on an ellipse whose major axis is AB the tangent at P meets the minor axis at Q. PA and PB cut the minor axis at R and T. Prove that Q bisects RT.

    I put $\displaystyle P(a\cos\theta,b\sin\theta)$ A=(a,0) and B=(-a,0)
    equation of tangent at P
    $\displaystyle bx\cos\theta+ay\sin\theta=ab$
    Point where tangent cuts minor axis, when x=o
    $\displaystyle y=\frac{b}{\sin\theta}{$
    $\displaystyle Q(0,\frac{b}{\sin\theta})$

    equation AP
    $\displaystyle y-0=\frac{b\sin\theta}{a\cos\theta-a}(x-a)$
    when x=0 $\displaystyle y=-\frac{b\sin\theta}{\cos\theta-1}$
    $\displaystyle R(0,-\frac{b\sin\theta}{\cos\theta-1})$

    equation BP
    $\displaystyle y-0=\frac{b\sin\theta}{a\cos\theta+a}(x+a)$
    when x=0, $\displaystyle y=\frac{b\sin\theta}{\cos\theta+1}$
    $\displaystyle T(0,\frac{b\sin\theta}{\cos\theta+1})$

    $\displaystyle RT=-\frac{b\sin\theta}{\cos\theta-1}-\frac{b\sin\theta}{\cos\theta+1}$
    $\displaystyle =-\frac{2b\sin\theta\cos\theta}{\cos^2\theta-1}$

    $\displaystyle RQ=-\frac{b\sin\theta}{\cos\theta-1}-\frac{b}{\sin\theta}$
    $\displaystyle =-\frac{b(2+\cos\theta)\sin\theta}{\cos^2\theta-1}$
    Now I don't know what to do. I can't show that RT=2RQ
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Jun 2009
    You have found the co-ordinates of R and T.
    Find the mid point R and T. That will be the co-ordinates of Q.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Nov 4th 2011, 06:42 PM
  2. show that a line bisects an angle ...
    Posted in the Geometry Forum
    Replies: 0
    Last Post: Feb 10th 2011, 07:20 PM
  3. Replies: 6
    Last Post: Jan 12th 2011, 02:38 PM
  4. Replies: 5
    Last Post: Nov 4th 2009, 06:49 PM
  5. Replies: 4
    Last Post: Mar 17th 2008, 01:53 PM

Search tags for this page

Click on a term to search for related topics.

Search Tags

/mathhelpforum @mathhelpforum