Conics - Standard parabola with two intersecting tangents

[prickles101]

Could you guys help me get started on this question?

The vertical chord with the equation x=a through the focus (a,0) - the latus rectum- of the parabola with the equation y²=4ax

Show that the tangents which pass through the end points of the latus rectum intersect at (-a,0)

[Crimson Sunbird]

 

[latex]y^2=4ax[/latex] [latex]\implies[/latex] [latex]2y\frac{\mathrm dy}{\mathrm dx}=4a[/latex] [latex]\implies[/latex] [latex]\frac{\mathrm dy}{\mathrm dx}=\pm 1\ \text{at}\ y=\pm2a[/latex]

The equation of the tangent through [latex](a,2a)[/latex] is [latex]y-2a=(+1)(x-a)[/latex] [latex]\implies[/latex] [latex]y=x+a[/latex] and the equation of the tangent through [latex](a,-2a)[/latex] is [latex]y+2a=(-1)(x-a)[/latex] [latex]\implies[/latex] [latex]y=-x-a[/latex].

 

Edited February 25, 2013 by imatfaal
Hidden with spoiler as it pretty much answers the question

[imatfaal]

Homework Help Rules

 

A simple reminder to all: this is the "Homework Help" forum, not the "Homework Answers" forum. We will not do your work for you, only point you in the right direction. Posts that do give the answers may be removed.

 

 

!

Moderator Note

 

 

Crimson Sunbird - nice answer, perhaps a bit too nice I have hidden it behind a spoiler in case other members can give a few hints and starters.

 

 

http://mathworld.wolfram.com/LatusRectum.html

http://en.wikipedia.org/wiki/Parabola#Coordinates_of_the_focus