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)

 

[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, 201312 yr by imatfaal
Hidden with spoiler as it pretty much answers the question

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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